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Paper Citation Record · LEDGER

Small Tamagawa numbers of elliptic curves with isogenies or torsion

As of 12 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2505.20479.

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

pith.paper-citation-record.v1
2505.20479 v2

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:05:55.992892Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

33 of 33 outbound references displayed

  • verified exact0
  • verified fuzzy14
  • unresolved19
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 372e414a-c4b3-48db-80b3-5fe534fc220b · outbound

This paper cites Barrios and J.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Barrios and J

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:06:02.683908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:53.870290Z digest=sha256:6ca2117db11e87fb88cfeb6a7dfda2c19ecd2dfb34b94e00539ce76a5ceceae7

Observation b789040f-61bc-499c-ab9a-bcbbadc9f039 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:06:02.504823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:53.952095Z digest=sha256:87595918e561fc5c47a124f95d988522e973b71588ae3900047e7aefdd702290

Observation 01fef23a-29d3-4d4c-b46d-2b41d971ec13 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:06:02.301800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.006465Z digest=sha256:644abd83b6ba69a2befe966fe623139f43d1d77a4053608da92d5c1b62e5d21e

Observation af403839-e29d-4727-89d4-8ab026c9f9be · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:06:02.070361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.084021Z digest=sha256:ec55b8104b51631f5c87ed030729e763b96d14c697fc7f16e01d0744410b3c8c

Observation e155d0a7-03ae-4348-9914-78df925f9a2d · outbound

This paper cites Comalada.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Comalada

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:06:01.792362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.135110Z digest=sha256:4b316bfd74899f6fb8d7ee9eb465e2b3cfaa2f63640e2bbb69fd77bc0e1d9122

Observation 5842cfa9-67b4-4d27-817f-a45e946fdb06 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:06:01.556500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.192150Z digest=sha256:460f002efddca6563aff93ce984a0e3c235d74bcedafb7460b62718aa970306b

Observation 6a055fd5-8f07-4307-84e5-ea8726f89c7f · outbound

This paper cites Dokchitser and V.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Dokchitser and V

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:06:01.236514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.263570Z digest=sha256:6f8613d3e022d19c747f24c27a32dabc3a7e998a9a55a510e0b5112f1e1ad105

Observation 9107c73a-d21c-4d35-be33-e8eed71477eb · outbound

This paper cites Notes on the Parity Conjecture , page 201–249.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Notes on the Parity Conjecture , page 201–249

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:06:00.906954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.341310Z digest=sha256:574284a07c66bbb2ab4c4f4b53fb36adfdc148ccfc5dad5d476626a7e02a9fea

Observation 96d5324a-3ef6-4c47-98c4-47ae5a687c6a · outbound

This paper cites Dummigan.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Dummigan

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:06:00.667840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.401399Z digest=sha256:de4a751759cfe0427d924222bf468a867674427c6b84b9ce07da5b07129fc7e4

Observation 03e96e64-e21c-44de-9c0a-7db1000f8cd0 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:06:00.308507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.452084Z digest=sha256:a9f72407cd5dd3f0a1cf95bcda1a142211ee80bd21613a64d0755b6c89295e7e

Observation 70d0028a-d553-4ec0-b408-d125051bcfdc · outbound

This paper cites Granville.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Granville

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:06:00.095370Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.515445Z digest=sha256:1bc2d2310cf57d923a8060df32c8759ff3ad7be7540cfd32c6bf3a1604a0c760

Observation 66584bd6-56d7-4ba0-8309-1f1da268e202 · outbound

This paper cites Halberstam and H.-E.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Halberstam and H.-E

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:05:59.848312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.594794Z digest=sha256:7999389171bf606e971f23936509fe7121f529124ee687e7aaec62b758936be5

Observation 400ef612-3855-424e-b545-8a3554744de0 · outbound

This paper cites Husemöller.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Husemöller

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:05:59.627308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.672911Z digest=sha256:77f55572deb1eac41f359d824c1b6c898398b709fd07dbf90a7e6ec99642608d

Observation 631a09d1-68e5-46c6-b5fd-46053f3bf054 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:59.424352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.740499Z digest=sha256:70eb756b1be834ce6b384019b10407a44e9d5b5a54cdd548c14b25d63df2a7bd

Observation 23400167-d3b4-4d67-a190-e8def937841d · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:59.141053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.810580Z digest=sha256:eed5af7ef6cc4fcf39fe02cb5048bfb91b995d0aca3816605f1c1f30e8bf7431

Observation 7e21ee82-9eeb-497a-918e-cbd1d41de2c6 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:58.826279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.911294Z digest=sha256:72b9020336e3b57968414b82a220cfd6d7362c1838dc0b82dc96882fab2b0905

Observation 74fdb3a0-4214-43b1-9e30-9f3b4a966bbc · outbound

This paper cites The L-functions and modular forms database.https://www.lmfdb.org, 2025.

Small Tamagawa numbers of elliptic curves with isogenies or torsion The L-functions and modular forms database.https://www.lmfdb.org, 2025

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:05:58.489579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:54.987578Z digest=sha256:0304b876c8f29f4f7a5e79ff4de1b890d970202d75067f0c0702df3d90b1813e

Observation 508f181f-5802-4662-8b59-7f2c8ced50c9 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:58.190388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.050348Z digest=sha256:f8be627faa64b70e56b2ff53df9b87a044de18ed9ad5358e348f55a101364bab

Observation 4154eb53-1ca3-4a3d-9677-3f00074f97fe · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:57.950886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.095662Z digest=sha256:33e4b2847f8ef3b1c5452dcaaf881f278e761fe12924860919c7d7223614e3a8

Observation e0b450bf-09ee-4d44-9666-5a850a8a4d68 · outbound

This paper cites Lozano-Robledo.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Lozano-Robledo

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:05:57.826637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.152459Z digest=sha256:e3a770a8b40f0f7197529580dfd3a35cc9dc52544d753bcadb7faaa5fe5a5de4

Observation 7de7ba1c-febc-4e90-bbae-1ccf2c2001df · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:57.711571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.202938Z digest=sha256:0a89f9bacc84843429f7f4cab2d63c9a1c4c8a93af9268e41b219a6f51eb8800

Observation 587d3f1a-f218-4418-8261-38355ba79c92 · outbound

This paper cites Melistas.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Melistas

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:05:57.573865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.250236Z digest=sha256:b45d7eb4c9cde09f8f500a98a799ed31534e53f85a22c06f1932afbc8dbeaf48

Observation c82cd644-e8bd-4fa9-af56-99191e5f0ce3 · outbound

This paper cites Melistas.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Melistas

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:05:57.476350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.302964Z digest=sha256:5fda0fa2f6be9ed36faf78f1c840e9a7befe067b34b259c553c7d2c6259d6f66

Observation f7a1c851-ea41-4952-beec-b31c428747a0 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:57.382312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.389244Z digest=sha256:d64041c1286ff9cdc630246fe48a6d2d1801ccdfe74a36cada3dc246629ba048

Observation f5e6d7f3-60c0-42cc-8fc0-fbebefcc3edd · outbound

This paper cites Papadopoulos.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Papadopoulos

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:05:57.235797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.434196Z digest=sha256:9a22f9fc1b9ae052c34daf0197f186bd7bb57afb4503822475bd433b50b20877

Observation 5bc469f5-ac25-4497-9999-1343ccf37a8c · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:57.050331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.521531Z digest=sha256:fb7ce367cc0fe13efb0aff5872d7dc65324d28ce1a112cc47a324064b4d9d4b6

Observation 5124f9a8-592c-425d-96ed-5498aa64dd77 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:56.906867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.562339Z digest=sha256:4c979a39f4b7ee778334051ca53c12c708b11200c4d7ab3172ecfd01072b8769

Observation d24f376b-0356-468a-8c8e-e43584f65a93 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:56.746715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.640437Z digest=sha256:a0c0e2ff40182b210d1ed9b881425889f129cd9ac055c9611f5819a2e3a94f0d

Observation d326a66f-81c0-40b5-b9c8-881db1e29e2d · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:56.604237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.721141Z digest=sha256:24d063faa0bf297756c6e3580a6c0533f37b38d9882c64b476c23124d34cc29d

Observation d8a498e4-7863-4832-8789-517915474879 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:56.499510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.778441Z digest=sha256:bbee2b765d8987fefdce49534094e2b8229f72bcadd397c3fa6b77667ad07cb5

Observation 908a2d0b-b9c2-4ff6-b593-c8c4c0beb110 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:56.362883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.844056Z digest=sha256:9b859363c6194e81f2a602eab7186a45146bc7f3c8efef523e3582e988947242

Observation 47b77971-8c64-4022-972a-3cf16b90cacc · outbound

This paper cites Tsukazaki.Explicit isogenies of elliptic curves.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Tsukazaki.Explicit isogenies of elliptic curves

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:05:56.256901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.925330Z digest=sha256:70e66f02f237fe79b3e0822acc6d8bd3b7c2bd836e78b17904351457f30ff7d6

Observation a47dd249-ab9e-4f56-ae53-64f815619389 · outbound

This paper cites an unresolved cited work.

Small Tamagawa numbers of elliptic curves with isogenies or torsion Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:05:56.145998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-07T14:05:55.992892Z digest=sha256:c344f80635e8c3edf103aa2fda3f63da61889c61561dd0b31798ca53f3a12913

Pith citing papers

No inbound Pith citation observations are available.