curve #4632

y² + xy = x³ + 258955790083729101225358987479265573521835x + 132667685967692661379063757692400324145069171670940647140673761

a-invariants: [1, 0, 0, 258955790083729101225358987479265573521835, 132667685967692661379063757692400324145069171670940647140673761]
c-invariants: [-12429877924018996858817231399004747529048079, -114624880676086459431492441829347851566051538476594212008248557385]
rank (lower bound): ≥ 18
torsion subgroup: ℤ/2ℤ
conductor (N): 1034003231463690975784539963190598608272398539684971850419967708743459786
discriminant (Δ): -8714874186082790065553583439918737859699810870740849753285732284210033501776918843215777499532990857848180602560729446103039488
Faltings height: 23.0400
naive height: 299.6091
primes of bad reduction: 2, 3, 7, 11, 17, 23, 37, 41, 43, 73, 101, 223, 227, 317, 359, 499, 619, 809, 1223, 1733, 3067, 3209, 9817, 10103, 11987, 20521, 70373, 230849
regulator: 179304439847952800633.75184583315001701911418926685829346144585112416328096
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:32:18 UTC
last updated: 2026-10-19 03:32:18 UTC

Witness: 18 independent points log in to add more points →

(-312934130582795947814, 4581117696465232693312041206431)
(-4572578694977430959029468272691833974/27545905800585649, -42176336596265194858497482580710189448648099276439370425/4571782774539539326170857)
(865993158399475613676, 31723305816137410025745479123991)
(1432815442936953651526, 58695966357836453120388483635083)
(2001324633162323169826, 93095802352019043187999189254583)
(38899458517668611737312784254898647447353213292/128052811584095957555219161, 22418885217811251870278552388991108791711286044404240752156520605143031/1449051022610705249764935320066096402659)
(-190545587991004003362166215464836936334/637539784874983225, 2721119644192760572438399368913368684080895441626097799531/509050580853988720193654125)
(286867235794451615176, 15184226317696191908418918624991)
(142726102552308300566209213969925582976349/581461804929330033424, -203677975252327242112455068097555319493258136530869786461154537/14021090357690651668911823467968)
(23910250932437631779758, 3698082909603433227600928413330559)
(61846130251937793271558, 15380966231673557329309826914705483)
(2005744871244073625600651914962889312/5705303126370849, 7043692170754970628669808409859480281200024404379167007/430941268367698088994993)
(2970178743949745721503493/16, 5118886673550759031192262587227907047/64)
(1615398040168658939946647586598194313017574063/5438426393821754456672004, 194749242752808272727094734908724747885343106457840917628929224318433/12682646348175601238295239872364233992)
(11713746529973541188334/25, 2361363286452796175104801556597367/125)
(1857567457229002126641202/1849, 2982083370097757207628788286131814661/79507)
(-799717245938602556617253533247678366/3065586079030225, -1168104217140655366185236771301872381128585458294513247/169734557643434554790375)
(201008937525969846990762082353989837889140386/1395834483176136574444225, -21687290375014640986298698088438617719175906914399163490050063824889/1649114782307560528032686426002606625)

Commentary

X660, T=3559/1077

last edited by Andrii Prokhorenkov at 2026-10-19 03:32:18 UTC · history