Paper Citation Record · LEDGER

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants

As of 19 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 1 inbound Pith citation observation for arXiv:2507.18574.

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

pith.paper-citation-record.v1
2507.18574 v3

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:32:22.961244Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-15T20:14:07.272953Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-15T20:16:34.078441Z

Reference resolution

23 of 23 outbound references displayed

verified exact3
verified fuzzy9
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a2c75487-6976-4816-8f33-2a66644150dc · outbound

This paper cites an unresolved cited work.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Unresolved cited work

Reference 1

Resolution: verified exact; doi, observed 2026-08-15T18:32:22.996791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c3099ffe-6dd0-40b2-b0b8-17f255ba0ca6 · outbound

This paper cites an unresolved cited work.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:32:23.315998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d9e43b7b-f9bd-40ea-8111-06470e0de2a7 · outbound

This paper cites Bell, Non-isomorphic abelian varieties with the same arithmetic, R.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Bell, Non-isomorphic abelian varieties with the same arithmetic, R

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:32:23.302016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0c78c401-04d1-44e7-bf76-06a2070d32b9 · outbound

This paper cites Dokchitser and V.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Dokchitser and V

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:32:23.287447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d53bd338-b4ac-410b-aff8-fa9925aa09f4 · outbound

This paper cites Gouvˆ ea and B.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Gouvˆ ea and B

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:32:23.274086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0b5c8103-b7af-4703-8d6e-91c9e2719a10 · outbound

This paper cites On the Joint Distribution Of $\mathrm{Sel}_\phi(E/\mathbb{Q})$ and $\mathrm{Sel}_{\hat\phi}(E^\prime/\mathbb{Q})$ in Quadratic Twist Families.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants On the Joint Distribution Of $\mathrm{Sel}_\phi(E/\mathbb{Q})$ and $\mathrm{Sel}_{\hat\phi}(E^\prime/\mathbb{Q})$ in Quadratic Twist Families

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:32:23.082704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bf697650-4f0f-46be-aef8-733d3c94815d · outbound

This paper cites Klagsbrun and R.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Klagsbrun and R

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:32:23.261278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1d7dd886-f8a7-408e-8e10-e0dac1c3d34e · outbound

This paper cites Kloosterman and E.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Kloosterman and E

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:32:23.247626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1db3adf7-7e03-4367-b6f3-1e4a5332a338 · outbound

This paper cites an unresolved cited work.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:32:23.234033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 38e29433-6217-4c62-81bc-4e9a4ef8955c · outbound

This paper cites an unresolved cited work.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:32:23.220119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ef8039e4-69cd-4c1d-91b4-46fa67440eb9 · outbound

This paper cites Monsky, Generalizing the Birch–Stephens theorem.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Monsky, Generalizing the Birch–Stephens theorem

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:32:23.205900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a73a4c55-3e23-418e-86d7-4e31cd31f04f · outbound

This paper cites Pal, Periods of quadratic twists of elliptic curves, with an appendix by A.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Pal, Periods of quadratic twists of elliptic curves, with an appendix by A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:32:23.192482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation af3edcb8-5365-4ee9-a780-ddb45139ecf1 · outbound

This paper cites Rubin, Tate-Shafarevich groups andL-functions of elliptic curves with complex multiplication, Invent.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Rubin, Tate-Shafarevich groups andL-functions of elliptic curves with complex multiplication, Invent

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:32:23.179974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0db665a1-d36e-4145-8a93-79b616b75c94 · outbound

This paper cites an unresolved cited work.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:32:23.167313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 449e264e-1847-4a09-93d2-c20095e5121f · outbound

This paper cites an unresolved cited work.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:32:23.153536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation da2f05a6-ccc5-43af-beb9-1981ef08d3cc · outbound

This paper cites Nontrivial torsion in the Tate--Shafarevich group of elliptic curves via visibility and twists.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Nontrivial torsion in the Tate--Shafarevich group of elliptic curves via visibility and twists

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:32:23.062259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f7ec5944-9c54-4f6d-a510-808b54efc02a · outbound

This paper cites an unresolved cited work.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:32:23.139136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f1643fb4-c634-4aba-a20b-3ae3e46f49db · outbound

This paper cites an unresolved cited work.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:32:23.124566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 72058f9d-c136-4e78-b078-f7992d12b5b6 · outbound

This paper cites The distribution of $\ell^{\infty}$-Selmer groups in degree $\ell$ twist families II.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants The distribution of $\ell^{\infty}$-Selmer groups in degree $\ell$ twist families II

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T18:32:22.943975Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a662b13d-3a48-422c-8059-a2078338d3cc · outbound

This paper cites The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T18:32:22.947839Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4f59bc5-ecfe-41d9-8ff6-80d36ea633c2 · outbound

This paper cites an unresolved cited work.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:32:23.110417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 54d97507-5bd4-4da2-a556-3f3502a4242f · outbound

This paper cites Tate, On the conjectures of Birch and Swinnerton-Dyer and a geometric analog, S´ eminaire Bourbaki, Vol.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Tate, On the conjectures of Birch and Swinnerton-Dyer and a geometric analog, S´ eminaire Bourbaki, Vol

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:32:23.096622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bfecc6d1-02e2-44d9-b527-c865902ac1a5 · outbound

This paper cites Rank one elliptic curves and rank stability.

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants Rank one elliptic curves and rank stability

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T18:32:22.961244Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 0b3574a4-fe2a-4e87-8539-e00e36f2a819 · inbound

Nontrivial torsion in the Tate--Shafarevich group of elliptic curves via visibility and twists cites this paper.

Nontrivial torsion in the Tate--Shafarevich group of elliptic curves via visibility and twists Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-07-07T03:18:47.816120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.