curve #4620

y² + xy + y = x³ + x² − 6131075764896307810013963249297695465x + 3377487873521287505410979026822967338989268597041517847

a-invariants: [1, 1, 1, -6131075764896307810013963249297695465, 3377487873521287505410979026822967338989268597041517847]
c-invariants: [294291636715022774880670235966289382321, -2918149522722392406882273154537714592491754837591041787369]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 236536244628704799119256780694743964878896550193854791627591910
discriminant (Δ): 9821924847788858647802620424555228441692126224342924920409259680287874483952603506653108538145424968135400040000
Faltings height: 20.1883
naive height: 265.7329
primes of bad reduction: 2, 3, 5, 11, 23, 43, 53, 71, 107, 113, 139, 149, 191, 263, 277, 311, 337, 401, 1723, 2777, 9173, 31601, 47969, 137453, 143813
regulator: 1532419737908410216.21572112465632959159081496602447239294531394677509820
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:30:33 UTC
last updated: 2026-10-19 03:30:33 UTC

Witness: 17 independent points log in to add more points →

(-105083178636645754035442286665651801511431596387/47387494539732485006366967184, 25412406520203777609063986311257904066004507938781624468296269113283683/10315626783306862108572284461266402814269248)
(-1660603900672404602840752843/617572201, -9966817968924605483925061311551706864954/15347286767051)
(-7217244304940080667/9, 75302454158707398708800940502/27)
(-3043023703598608537/4, 22056586026637348205622670563/8)
(937884778393192295/4, 11179460241956447253670538979/8)
(583137156281170157, -22912020575782053316907904)
(5065782008543711275/9, -8742616701413328500723085184/27)
(-17083971513602174641568174323/6339185161, -288711931581758659493609383317299990707986/504719583333659)
(2558448105388430691, 2106696868668418962333789244)
(23922276502498733803/9, 65361337681953961839838556452/27)
(-4248474085237120199075216162955707/1778985118052289, -157379045031110373341032143253701894113213409804112/75034064551956452330913)
(15100263084152767539745327038350167/82360901633063881, -35529893247811605790621838590262260386298342174650384/23636416738728192948702971)
(-17366771202666893087/9, -76478260313683230274339510408/27)
(-12632798732124124737789398162764667/13176875649668329, -4377148478568184525919589743176068265806193756180448/1512581106175174745862517)
(-396207759536133117745793/201601, 253389288911506027997554917841911104/90518849)
(4757663612458388836313/289, -324556148722860173937486225799512/4913)
(47627999564252139289947/11881, -8513828529932335401225106464046496/1295029)

Commentary

X400, T=-577/3960

last edited by Andrii Prokhorenkov at 2026-10-19 03:30:33 UTC · history