curve #311

y² + xy = x³ − 47272342688123468294792417941461088407840527939755x − 42941508837775730432220302570878099751385660941354601764714541918970825039

a-invariants: [1, 0, 0, -47272342688123468294792417941461088407840527939755, -42941508837775730432220302570878099751385660941354601764714541918970825039]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 25725142933318819706009609339333397294766021498979988120833604560475705134314952598
naive height: 354.7536
Faltings height: 27.6235
discriminant (Δ): 5964254353060440281776945916503620086821580011305699112141314114279612506639005884799439060156150387371657313705870470386745717322956901121284033068032
primes of bad reduction: 2, 3, 7, 11, 17, 29, 31, 41, 47, 53, 79, 107, 109, 137, 149, 181, 313, 487, 2063, 3209, 3329, 6469, 10513, 15091, 18913, 23417, 32441, 47051, 131749, 643889
regulator: 10662164547009989409044.141281706634126087725974780397213267998544177
submitted by: 7fff-zip
submitted at: 2026-08-24 00:23:49 UTC
last updated: 2026-08-24 00:23:49 UTC

(89873999762568780808944086, -849500431278230131468408087958099419087)
(450127354986660415882556542/9, -9457669964200507094600383360157495851109/27)
(76036685752527470559988976, -660283744951480008502064211620008271689)
(61764401751121059885310958, -482347076966221958676061706248568416447)
(3284422587924885408030114638/121, 181882420506654348275707260415779062335219/1331)
(7428570924588756205375238, -3978481790272887803165941078674026671)
(-201523342589791079432589178/49, -3104328774986118421284712023478884727993/343)
(11669604067718256381160316, -31536830411141643423399302578679164687)
(11148107237831828525753104402/729, -1043448966462230394289562790046533786261893/19683)
(1407862139449395580553361251362/3969, -1670161187070125076360716367242985381688678729/250047)
(37098420262985689289037181406/5041, 996122886052897718977976515513302939699031/357911)
(20137718149475453258700204614/1369, 2504417159734057540134232771804138721992589/50653)
(246888350148643697437623194/25, -2661478355922751021511873675640357089963/125)
(6912927404521945743128465386382/851929, 8162637195113372140337291792720894104803588451/786330467)
(-168850967572341818143988244070606/38278969, -2114998569238413252000668852972626577014189079761/236831981203)

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