curve #6536

y² + xy + y = x³ − x² − 9730454040442129912098300734073780x + 350165566957252455352524276794482967983682539565847

a-invariants: [1, -1, 1, -9730454040442129912098300734073780, 350165566957252455352524276794482967983682539565847]
c-invariants: [467061793941222235780718435235541425, -302543049851066119322802902414933223324668755624955625]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 588574279643154047521915100938104399272722122250320638016664981116704330068045160117150
discriminant (Δ): 5992882565566586117464584076119342731562677725995219443732649368064488281110009450635933381173504000000
Faltings height: 18.4745
naive height: 246.3953
primes of bad reduction: 2, 5, 11, 13, 19, 61, 71, 1147669, 10716883, 117329302450688311718871408429629, 693205219738118050948801080129923
regulator: 3817722010490776527248840.5688638195777842663988656180409901374404326308747000013214435
submitted by: apkorte
submitted at: 2026-11-04 10:35:07 UTC
last updated: 2026-11-04 10:35:07 UTC

(73800050853929669, 5831437766935365779865965)
(13171981278918032091/289, -5715388663459915577093890955/4913)
(68124543549262469, -1856249272647093356103635)
(196648154611103243, -77724973901319486265404379)
(2934812827110781509, -5024908631438269716020961555)
(122073717024929029, -31328493095574609152754515)
(-45708346935996671, -26446781181159114138842315)
(101074874961718979, 19981372251404507706375335)
(5757993027184759843/81, -3065397489109478817637860691/729)
(-20272364158961581, -23218388533595555854869385)
(43254406674043229, -3194856871502988150452315)
(71156043451001509, -4249822599244172489339955)
(396060406366173331/9, -72364374487348145834801785/27)
(21304551077507109, 12350400974902441331060045)
(313970047588013521/9, -196876162116563801626401145/27)
(67653732842240229, -1231677399847509527859315)
(-79444156795110891, -24935747270143151130865155)
(75946667165287759, 7015875501849069765382195)
(-113079896898261931, 2127094699619247859257965)
(1096586779742687809/25, -347930830811404148921927887/125)
(118376860598920979, 29276774291369233050554935)
(71848545507075229, -4684456032947077304669315)
(19866617468996259, -12833369200442655267856555)
(-88337897869447379/9, 569391203403899720216641055/27)

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