Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T14:29:42.513949Z
Paper Citation Record · LEDGER
Selmer groups of families of elliptic curves with an $\ell$-isogeny
As of 21 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 1 inbound Pith citation observation for arXiv:2508.21406.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-01T03:55:48.921447Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-01T11:45:47.030161Z
Reference resolution
40 of 40 outbound references displayed
- verified exact1
- verified fuzzy15
- unresolved24
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation a77938c2-a9ec-40ed-8dca-aa0e57036f35 · outbound
This paper cites Integers expressible as the sum of two rational cubes.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Integers expressible as the sum of two rational cubes
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T14:29:38.318742Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6021e200-3cb1-47bd-8b91-ab3bfd70c3eb · outbound
This paper cites Counting 5-isogenies of elliptic curves over $\mathbb{Q}$.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Counting 5-isogenies of elliptic curves over $\mathbb{Q}$
Reference 2
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T14:29:42.834685Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ed78966c-3eef-4e0d-b903-beb640eda869 · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:50.887752Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 852d0449-5097-4da8-b520-8b59f456c27e · outbound
This paper cites The average number of elements in the 4-Selmer groups of elliptic curves is 7.
Selmer groups of families of elliptic curves with an $\ell$-isogeny The average number of elements in the 4-Selmer groups of elliptic curves is 7
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T14:29:38.668919Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cb073b82-ff90-4277-92f2-4a23cd0e67f3 · outbound
This paper cites The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1.
Selmer groups of families of elliptic curves with an $\ell$-isogeny The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T14:29:38.757818Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cfdad7af-f0f4-4e4e-b302-0afcaead530b · outbound
This paper cites Bhargava and A.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Bhargava and A
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T14:29:38.875344Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e15e6a0d-8abe-422c-9ee8-2efedde74d00 · outbound
This paper cites Bhargava and A.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Bhargava and A
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:50.666267Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c266bf16-1210-4992-bfc6-070108778f5c · outbound
This paper cites Boggess and S.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Boggess and S
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:50.434947Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 7b059c25-6d1d-4cd2-8e44-046c9d63e284 · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:50.251577Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b13fa6a2-22ee-4075-9f1a-d484a7bf5a90 · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:50.014348Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f2bb6a38-e7a7-4fb3-88ad-c4a005c682f0 · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:49.795905Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation fdfc798e-1077-477e-96a5-1a682c2b41f9 · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:49.519707Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e0f7c36f-facd-4621-9fe6-0b10f17a2fc7 · outbound
This paper cites Cullinan, M.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Cullinan, M
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:49.292414Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 77f04bb7-43a6-41ab-b59a-357069da00a2 · outbound
This paper cites Davenport.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Davenport
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T14:29:39.685643Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1664131b-d90a-4365-9073-7bcc52c50e43 · outbound
This paper cites Dokchitser and V.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Dokchitser and V
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:49.063840Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 79cdb1f6-952b-4a3f-9117-82122a761c9e · outbound
This paper cites Granville and K.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Granville and K
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:48.811168Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ccc9ac2b-814f-4ccd-8436-14f605c631dc · outbound
This paper cites Harron and A.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Harron and A
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:48.549664Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 5cb349be-4edc-4617-a370-ed152420391d · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:48.310743Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ed193cf0-ac29-40a4-92eb-12bb220950e8 · outbound
This paper cites Iwaniec and E.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Iwaniec and E
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T14:29:40.166726Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bbe8b5e0-8880-46d0-a16a-7150e8534f7f · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:48.057508Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 110fd61b-4f08-4330-ae58-3d352a7267f8 · outbound
This paper cites Klagsbrun and R.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Klagsbrun and R
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:47.856662Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 5af0adea-fd21-45ca-9114-f35ebb78e379 · outbound
This paper cites Klagsbrun and R.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Klagsbrun and R
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:47.642585Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 935ef84f-3be7-4f93-b402-1613fd44db33 · outbound
This paper cites Kowalski.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Kowalski
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:47.432541Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation bcf30715-8004-4e2a-afb9-f4ea3139378d · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:47.168668Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 2daf5f68-fe27-4eb4-8ce8-502197828562 · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:46.950032Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f1d638d9-4cbe-4baf-b87d-3e678600a2db · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:46.706743Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 04951b45-b5e7-4d94-8845-a2b17ea371f6 · outbound
This paper cites Molnar and J.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Molnar and J
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:46.512186Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 76e062ed-d5ca-4bb9-a66a-85bb5da0d3f2 · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:46.271814Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d655b126-08ab-4ce6-a753-880e1b98e446 · outbound
This paper cites Pizzo, C.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Pizzo, C
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:46.052377Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9561c32e-b110-45c1-89cc-2a54ce5dde46 · outbound
This paper cites Pomerance and E.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Pomerance and E
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:45.806934Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 2c4dcc6a-fd1d-4493-985f-338eb560928b · outbound
This paper cites Poonen and E.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Poonen and E
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:45.516254Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation da3c4649-76af-41cf-9737-55e13d177f3e · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:45.251601Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation dc728972-c115-4b4c-ba0f-4e7afef05d28 · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:44.994138Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 7e7dcac5-f768-40cc-a318-267c128ee9f8 · outbound
This paper cites Serre.Lectures onNX (p), volume 11 ofChapman & Hall/CRC Research Notes in Mathematics.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Serre.Lectures onNX (p), volume 11 ofChapman & Hall/CRC Research Notes in Mathematics
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:44.713038Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 5d3cb2e6-9ca1-4df6-af76-8ba38c213b04 · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:44.467345Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 516c58bd-c049-41cb-b2bf-9bf57075549d · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:44.180416Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a9b6f31a-f749-4934-9708-f6eda172ae15 · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:43.859278Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b4bd5c46-93d2-48b1-8800-3db76c3458e6 · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:43.486906Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 06a4969d-f097-4bcc-bb8c-42fb9311ed1a · outbound
This paper cites an unresolved cited work.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Unresolved cited work
Reference 39
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T14:29:43.256116Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a3719ee4-07cf-4fca-9da4-26e7cb063dd0 · outbound
This paper cites Xiong and A.
Selmer groups of families of elliptic curves with an $\ell$-isogeny Xiong and A
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T14:29:43.035055Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Pith citing papers
Observation bae83e1b-b3d8-4bdf-9fb2-929c05fc4bb8 · inbound
Tamagawa ratios and unbounded Selmer moments cites this paper.
Tamagawa ratios and unbounded Selmer moments Selmer groups of families of elliptic curves with an $\ell$-isogeny
Reference 17
- Resolution
- verified exact
- arxiv_id, observed 2026-07-01T11:45:47.031693Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.