Paper Citation Record · LEDGER

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields

As of 15 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:1909.00637.

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

pith.paper-citation-record.v1
1909.00637 v2

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T05:59:15.037653Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+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

34 of 34 outbound references displayed

verified exact2
verified fuzzy21
unresolved11
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External citation measurements

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Outbound references

Observation 0517d747-bf3c-49a9-9078-c73f864ae89f · outbound

This paper cites Bosma, J.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Bosma, J

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.475746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 94d2aba7-7f7a-4804-8ae5-c57c5fcfabfe · outbound

This paper cites Bourdon, P.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Bourdon, P

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.463139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2d6ae83f-584c-4497-aaa0-66bd32725787 · outbound

This paper cites Bourdon, and P.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Bourdon, and P

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.447379Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 055e4c5b-31cc-4d07-b450-538d79a801cd · outbound

This paper cites Chou, Torsion of rational elliptic curves over quartic Galois num ber ﬁelds.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Chou, Torsion of rational elliptic curves over quartic Galois num ber ﬁelds

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.432965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8b7345ed-778c-4df7-b836-c3f0d5967cbe · outbound

This paper cites Bounds for torsion on abelian varieties with integral moduli.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Bounds for torsion on abelian varieties with integral moduli

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:59:15.095942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation da9d009a-16ac-4e7c-ab40-c9d84cf0a8bc · outbound

This paper cites an unresolved cited work.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:59:15.419687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3ec715dd-ef66-4e1f-bd69-065e0236e6b6 · outbound

This paper cites an unresolved cited work.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:59:15.406654Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0e73e94d-1013-44ba-8361-b104401a8404 · outbound

This paper cites Sporadic Cubic Torsion.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Sporadic Cubic Torsion

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:59:15.078620Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 32392929-c2e4-4d8e-a749-71c5c3a15386 · outbound

This paper cites an unresolved cited work.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:59:15.395366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation add0adc3-c47e-4f10-b4b2-b20a22c4def7 · outbound

This paper cites Dieulefait, E.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Dieulefait, E

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.384848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation bf0d05c1-c47b-4c8b-a3c4-45994b4668eb · outbound

This paper cites an unresolved cited work.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-14T05:59:14.951673Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b4d6130-89d9-49ea-9241-3cc2e5fcee28 · outbound

This paper cites an unresolved cited work.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:59:15.366618Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4fed64ad-8c55-4d8b-a627-46dd54550838 · outbound

This paper cites Gonz´ alez-Jim´ enez,Complete classiﬁcation of the torsion structures of ration al elliptic curves over quintic number ﬁelds.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Gonz´ alez-Jim´ enez,Complete classiﬁcation of the torsion structures of ration al elliptic curves over quintic number ﬁelds

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.354942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation de158b84-6fb3-4a6a-8ff4-b9bacb440300 · outbound

This paper cites Explicit char- acterization of the torsion growth of rational elliptic cur ves with complex multiplication over quadratic ﬁelds.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Explicit char- acterization of the torsion growth of rational elliptic cur ves with complex multiplication over quadratic ﬁelds

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.341378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c81f3d37-e982-4ddb-bfb0-36cdfcc90912 · outbound

This paper cites Gonz´ alez-Jim´ enez,Torsion growth over cubic ﬁelds of rational elliptic curves with complex multiplication.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Gonz´ alez-Jim´ enez,Torsion growth over cubic ﬁelds of rational elliptic curves with complex multiplication

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.327856Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 65eb3bfe-73ca-4d93-8ad7-dab5adb62647 · outbound

This paper cites Gonz´ alez-Jim´ enez,Torsion of rational elliptic curves with complex multiplic ation over number ﬁelds of low degree.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Gonz´ alez-Jim´ enez,Torsion of rational elliptic curves with complex multiplic ation over number ﬁelds of low degree

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.314584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 7403a173-16f7-4520-a604-b5571ee01ab2 · outbound

This paper cites Gonz´ alez-Jim´ enez, and ´A.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Gonz´ alez-Jim´ enez, and ´A

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.301762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ee95080e-21dd-4453-952c-b6008e9d4277 · outbound

This paper cites Gonz´ alez-Jim´ enez, and F.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Gonz´ alez-Jim´ enez, and F

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.289023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5f794a6c-d62b-4d6b-8d18-3c325a4e1040 · outbound

This paper cites Gonz´ alez-Jim´ enez, and F.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Gonz´ alez-Jim´ enez, and F

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.275595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 33218533-2794-4632-9117-d47752bac8bc · outbound

This paper cites Gonz´ alez-Jim´ enez, F.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Gonz´ alez-Jim´ enez, F

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.263613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation abdb539f-8bec-44d5-82c4-d4dc14a378e1 · outbound

This paper cites Gonz´ alez-Jim´ enez, and J.M.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Gonz´ alez-Jim´ enez, and J.M

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.251254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 05f61c33-4403-439d-bc6c-488a510b8252 · outbound

This paper cites Gonz´ alez-Jim´ enez, and J.M.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Gonz´ alez-Jim´ enez, and J.M

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.237398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b5ba2e85-0da7-4624-af89-30d30d87487f · outbound

This paper cites Guˇ zvi´ cTorsion growth of rational elliptic curves in sextic number ﬁelds.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Guˇ zvi´ cTorsion growth of rational elliptic curves in sextic number ﬁelds

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.224641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation fae6b49d-723e-4efe-959f-bbda15301d21 · outbound

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

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Kamienny, Torsion points on elliptic curves and q-coeﬃcients of modular forms

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-14T05:59:14.999484Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 49cbd867-a962-4b99-8168-09879a7a54d4 · outbound

This paper cites an unresolved cited work.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-14T05:59:15.003071Z

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Unavailable: canonical work link unavailable.

Observation 6e4e9400-b4fa-4782-b17e-1e52ffcf8fd4 · outbound

This paper cites Mazur, Rational isogenies of prime degree.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Mazur, Rational isogenies of prime degree

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-14T05:59:15.006458Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42fb9758-db24-4cee-9e32-275fca496a20 · outbound

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

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Merel, Bornes pour la torsion des courbes elliptiques sur les corps de nombres

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.187088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 205a9cb6-0b4e-48fc-836d-4942ebef12ec · outbound

This paper cites M¨ uller, H.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields M¨ uller, H

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-14T05:59:15.013832Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f78968de-a106-42ca-a6fe-76ad0ab23325 · outbound

This paper cites Najman, Torsion of elliptic curves over cubic ﬁelds and sporadic poi nts on X1(n).

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Najman, Torsion of elliptic curves over cubic ﬁelds and sporadic poi nts on X1(n)

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.167744Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 458eedb0-4337-4e36-aadb-f627681f9ef8 · outbound

This paper cites Olson, Points of ﬁnite order on elliptic curves with complex multip lication.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Olson, Points of ﬁnite order on elliptic curves with complex multip lication

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.155438Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 52216a01-d727-4e4c-9479-1b6baa137e32 · outbound

This paper cites Petho, T.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Petho, T

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-14T05:59:15.025409Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation df164129-4f9b-4e02-b132-50dcfc94764b · outbound

This paper cites Silverman, The arithmetic of elliptic curves.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Silverman, The arithmetic of elliptic curves

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.132868Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a3c02c75-8f39-4420-a0fe-635d380037a4 · outbound

This paper cites Silverman, Advanced topics in the arithmetic of elliptic curves.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Silverman, Advanced topics in the arithmetic of elliptic curves

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:15.119675Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d005c791-ebfe-427f-b1f6-06c770d9dfa1 · outbound

This paper cites an unresolved cited work.

Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:59:15.107264Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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