curve #4130

y² + xy + y = x³ − 1389931819058221224568092008155355389053x + 31268758710668100695318540355099554098730716729426452295948

a-invariants

[1, 0, 1, -1389931819058221224568092008155355389053, 31268758710668100695318540355099554098730716729426452295948]

c-invariants

[66716727314794618779268416391457058674521, -27016207526017239000855293957778206669472241878811640371711069]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

4314840781331577048533982362444226180847473271945109203486392757751509762883515395627329659613705975331330

discriminant (Δ)

-250527312583916610737967422281900878165744280161937646698986212727951060566825820758302156847006805311918556974189062500

Faltings height

21.6082

naive height

282.9031

primes of bad reduction

2, 3, 5, 7, 29, 31, 3001, 119831216174217960033270873519462043, 63555015044788012585684111936661836657486223912739261314772689

regulator

359087157220808323009832048060.936418382730185794264020863223919616906103422424287793253574

submitted by

apkorte

submitted at

2026-10-10 11:14:43 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-10 11:29:53 UTC

Witness: 26 independent points log in to add more points →

(30966147068942497649, -133870960745661716903409393450)
(-41348946710236762213, -134332489462530028097645996268)
(23024657545057022149, 107108487310893596450609696300)
(43582499655292433714, -231244782392282148391901539710)
(-3211592811572101, -176842366546235379325976035200)
(5199844624287472649, 155505384500673488017679620800)
(95534421153001386224, 877729132422659177061536575500)
(13911711296587462049, -120933210754781603840569063800)
(229621741478943008231/4, -3000288746944628783022968829915/8)
(75535333247636317049, -597706598977862313203628415050)
(-179064811783544602034/9, -6100268205829536404294529509150/27)
(61309848820464442274, 420130563360165985774328596050)
(3345308520098747529074, -193476167049459361882313230943925)
(84126703729163063324, 713952721434954935490212753475)
(-6553559837062003351, -200240580935041957016117335200)
(97715416008455349676904/3721, -25758169893539018446794928224087900/226981)
(-7037505299474175226, -201747040574085290463013208325)
(10989650803467243587909/16, 1150419265443654982618203778739175/64)
(2330949596334615543524, 112523777496483744506745500916675)
(3657891257351755603637/361, -925974589141668274962371233989492/6859)
(469603404264671418524, -10145883390306512692677679163325)
(131084426706615303254, -1449658816835554064980303353285)
(93428523905217832274, 846721147982899874419662441675)
(8148228613865743681421/529, 1414409663312248258706608108317900/12167)
(20318276365653757154, -106844661797514388339560371445)
(51149183195095111239146/4489, 39111615761962504587078529659947145/300763)

Commentary

Specialization at T = 799/404 of the rank-17 fibration of X1008 given in curve#3594. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-10 11:14:43 UTC · history