Paper Citation Record · LEDGER

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$

As of 18 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2507.13199.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2507.13199 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:36:44.602134Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

40 of 40 outbound references displayed

verified exact2
verified fuzzy35
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7005aa3b-91f6-48b1-8468-1288f99fbc53 · outbound

This paper cites The Magma algebra system. I. The user language.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ The Magma algebra system. I. The user language

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:50.447005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 571ac6b5-1128-433a-9de7-7289b9389803 · outbound

This paper cites On the level of modular curves that give rise to isolated j-invariants.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ On the level of modular curves that give rise to isolated j-invariants

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:50.261053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 44ed5189-bbc9-421c-9cef-cfbe02300c1c · outbound

This paper cites Towards a classification of isolated j-invariants.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Towards a classification of isolated j-invariants

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:50.011486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 30a7c5bd-97a9-424f-b333-2968b3b412d8 · outbound

This paper cites Torsion of rational elliptic curves over quartic Galois number fields.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Torsion of rational elliptic curves over quartic Galois number fields

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:49.757558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 80fa64b9-fe75-475a-9139-b6eb5db031bf · outbound

This paper cites Torsion points on curves and p-adic abelian integrals.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Torsion points on curves and p-adic abelian integrals

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:49.475384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7047e209-98cb-4b98-9e90-db847e0c5d21 · outbound

This paper cites Congruence subgroups of PSL(2 , Z) of genus less than or equal to 24.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Congruence subgroups of PSL(2 , Z) of genus less than or equal to 24

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:49.253970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bc68b67f-f292-42f9-9b19-efe8010e415d · outbound

This paper cites Les sch´ emas de modules de courbes ellip- tiques.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Les sch´ emas de modules de courbes ellip- tiques

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:48.990110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e06888f9-bad0-4420-9b51-a03a5661b2bc · outbound

This paper cites Sporadic cubic torsion.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Sporadic cubic torsion

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:48.794913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 52072de1-59d8-4541-94ed-3eb03830c5b9 · outbound

This paper cites Torsion subgroups of elliptic curves over quintic and sextic number fields.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Torsion subgroups of elliptic curves over quintic and sextic number fields

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:48.662406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 08bddc2c-7007-463e-8310-61507e7856b0 · outbound

This paper cites A first course in modular forms.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ A first course in modular forms

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:48.506719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cde6aac3-d522-411b-a9da-58ead4f18a16 · outbound

This paper cites Complete classification of the torsion structures of rational elliptic curves over quintic number fields.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Complete classification of the torsion structures of rational elliptic curves over quintic number fields

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:48.378893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1573e394-59c2-4539-bb16-d259aeec50f5 · outbound

This paper cites Growth of torsion groups of elliptic curves upon base change.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Growth of torsion groups of elliptic curves upon base change

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:48.150677Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c82729a9-2e20-4147-95a7-e6338ccbc43a · outbound

This paper cites Torsion growth of rational elliptic curves in sextic number fields.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Torsion growth of rational elliptic curves in sextic number fields

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:47.998812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ecca32f8-4976-4b60-880e-6a4d3387d6bc · outbound

This paper cites Torsion growth over number fields of degreepq.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Torsion growth over number fields of degreepq

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:47.826117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4e87b1f6-d453-41f9-b9f2-5ae8dbb00ec0 · outbound

This paper cites On the torsion of elliptic curves over cubic number fields.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ On the torsion of elliptic curves over cubic number fields

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:47.679365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3523c490-e0ea-4294-b7f2-b828c740d679 · outbound

This paper cites Torsion points on elliptic curves and q-coefficients of modular forms.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Torsion points on elliptic curves and q-coefficients of modular forms

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:47.517533Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 68b9c1b2-0df3-461d-bef7-d64af81e39ba · outbound

This paper cites Torsion points on elliptic curves defined over quadratic fields.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Torsion points on elliptic curves defined over quadratic fields

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:47.371088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8e40ab1b-b14b-4ba1-a22a-057414957334 · outbound

This paper cites p-adic numbers, p-adic analysis, and zeta-functions.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ p-adic numbers, p-adic analysis, and zeta-functions

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:47.206698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d83b0606-820f-4308-a9ed-66f1e28047bb · outbound

This paper cites Finiteness of E(Q) and X(E, Q) for a subclass of Weil curves.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Finiteness of E(Q) and X(E, Q) for a subclass of Weil curves

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:47.061488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 22b50b28-b5fa-488d-92a6-006db8a6f5c3 · outbound

This paper cites The L-functions and modular forms database.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ The L-functions and modular forms database

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:46.978885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 381eb9d8-01b3-40c5-97c3-33e5ee0c062d · outbound

This paper cites Modular curves and the Eisenstein ideal.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Modular curves and the Eisenstein ideal

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:46.859824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 32ec2bcf-0509-47c5-a8fe-28cfb18db002 · outbound

This paper cites The method of Chabauty and Cole- man.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ The method of Chabauty and Cole- man

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:46.741611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9867d9c8-022d-439b-843d-565383a783a4 · outbound

This paper cites Bornes pour la torsion des courbes elliptiques sur les corps de nombres.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Bornes pour la torsion des courbes elliptiques sur les corps de nombres

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:46.624447Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7c20d050-483d-4011-8d69-10a0892b7303 · outbound

This paper cites Jacobian varieties.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Jacobian varieties

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:46.501425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 48836b5c-2db3-40ce-b826-3b8e8aa8abd6 · outbound

This paper cites Torsion of rational elliptic curves over cubic fields and spo- radic points on X1(n).

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Torsion of rational elliptic curves over cubic fields and spo- radic points on X1(n)

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:46.407681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 620c021b-920a-4320-9d3b-c623c6ff1be9 · outbound

This paper cites ℓ-adic im- ages of Galois for elliptic curves overQ (and an appendix with John Voight).

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ ℓ-adic im- ages of Galois for elliptic curves overQ (and an appendix with John Voight)

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:46.318073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f01d307c-87c4-47f8-9e48-ea954b4294ce · outbound

This paper cites Elliptic curves over Q and 2-adic images of Galois.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Elliptic curves over Q and 2-adic images of Galois

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:46.223905Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 204c46f7-2d5e-4928-894c-0bb0edb52f70 · outbound

This paper cites Propri´ et´ es galoisiennes des points d’ordre fini des courbes elliptiques.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Propri´ et´ es galoisiennes des points d’ordre fini des courbes elliptiques

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:46.125828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 514bae88-f51e-41eb-89ab-aaf7b15ab81e · outbound

This paper cites Topics in Galois theory.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Topics in Galois theory

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:46.031605Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 204d7ebd-0ea3-4081-9a80-29ab8a2cfba7 · outbound

This paper cites Silverman.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Silverman

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:45.927015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ea24aaff-f727-4872-a821-eed2d3c2bdb5 · outbound

This paper cites Isolated points on modular curves.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Isolated points on modular curves

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:45.787963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation dd3f9a00-4b93-4eaa-983b-47e6f204fe80 · outbound

This paper cites Isolated and parameterized points on curves.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Isolated and parameterized points on curves

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:45.605622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 71561559-9f3d-4d7b-80d3-647b7c1d4799 · outbound

This paper cites L’arithm´ etique sur les courbes alg´ ebriques.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ L’arithm´ etique sur les courbes alg´ ebriques

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:45.474808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ef04c972-0301-4ce2-ac6b-cbdf413a2b05 · outbound

This paper cites Computing actions on cusp forms.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Computing actions on cusp forms

Reference 34

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:36:44.951719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6c9e0a82-49fb-4949-90ef-735efd53b887 · outbound

This paper cites Computing actions on cusp forms.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Computing actions on cusp forms

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:45.308092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 56577c2c-873d-44f7-8ddc-47d6097974b1 · outbound

This paper cites Explicit open images for elliptic curves over $\mathbb{Q}$.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Explicit open images for elliptic curves over $\mathbb{Q}$

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-06T16:36:44.381814Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 26e00e77-e48b-414e-a652-f9394fea6bc2 · outbound

This paper cites On the possible images of the mod ell representations associated to elliptic curves over Q.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ On the possible images of the mod ell representations associated to elliptic curves over Q

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-06T16:36:44.469132Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95aa5bcf-dc19-415c-a52b-4c7150eae140 · outbound

This paper cites Open image computations for elliptic curves over number fields.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Open image computations for elliptic curves over number fields

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:36:45.166360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 87ecbe9f-2ec1-423e-86d1-2c388b84de72 · outbound

This paper cites Possible indices for the Galois image of elliptic curves over Q.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Possible indices for the Galois image of elliptic curves over Q

Reference 39

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:36:44.789906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fcea2623-a662-4462-8c6d-6fb9ddd913aa · outbound

This paper cites an unresolved cited work.

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$ Unresolved cited work

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-06T16:36:44.143901Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

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