curve #5410

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y² + y = x³ + 333724390317052069118188688416567810

a-invariants: [0, 0, 1, 0, 333724390317052069118188688416567810]
c-invariants: [0, -288337873233932987718115026791914588056]
rank (lower bound): ≥ 15
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 906640482317727900023195951228507775255643978301336452058030912615361
discriminant (Δ): -48112690475154866470530939543843222109491258996517021501363526439759362187
Faltings height: 12.8172
naive height: 177.1144
primes of bad reduction: 3, 7, 19, 4729, 9829, 122693, 913527311, 14485206383
regulator: 30185210055367642778479.320996525516807845142172274976852821494318231
submitted by: Maksym Voznyy
submitted at: 2026-10-21 21:54:05 UTC
last updated: 2026-10-21 21:54:05 UTC

Witness: 15 independent points log in to add more points →

(-278743676960/9, 15596904266696032795/27)
(18834549059194/9, 83214526985252211554/27)
(-307019182130, 552072932943146710)
(85209231170, 578224058281156710)
(380670683128, 623608405443563521)
(-91907577020, 577016504759227585)
(-388007052352, 524700041158108673)
(1481483222800/169, 1269183651899985860245/2197)
(-2210707582160/81, 421122333155650357465/729)
(216950756116840167353756079587252335001635788625/3882842744086681713817243744811584, 101051361094069524439685820432050808582726696130991284319145632922963545/241949485446458180694944249323491198347801581655552)
(32139468149803146033795567424482746486668/30673852483064909847376756761, 6544447560553034574291648099830049382024384955633889958226374/5372203889513780546154668113839865350160509)
(-32416006391644115845812162708571852307932/71390614364937762732278900281, 9346830242665431838566828604627005224703089925154935649972141/19074874051791711357042188949280076093667821)
(25392213228170970891549598411869080846492/14184972607880140677877497529, 4162272942983980343864818987835720701280203075007542765557741/1689439920981040507939135057521587477439917)
(2518111751074116112808545627445451043765900/5335750948190877146862019393681, 8164751506899257361027229408515128686262287414734459901182239410/12325181555260365576752261680482503905987145671)
(11401461207820022047056526275773176438945/1932243415538476102526919744, 1218409335332130546108609016654302638720945507011718610610033/84936185736566991034655525142614961065472)

Commentary

Reynya - Voznyy (2026), 3-isogenous to curve#5411

last edited by Maksym Voznyy at 2026-10-22 12:49:03 UTC · history