curve #6345

y² + xy = x³ − x² − 16858866801094717174565334680664355x + 962774838292786979430974099838227286106172797682425

a-invariants: [1, -1, 0, -16858866801094717174565334680664355, 962774838292786979430974099838227286106172797682425]
c-invariants: [809225606452546424379136064671889049, -831837460284967946586846393223769465489621006174114493]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 40681424041075818849827532230199658745116618678059519847436108689642849175467404053890
discriminant (Δ): -93770452767216884385764178267837552460142608077107675671053323598418410766542035659989296388200120873300
Faltings height: 18.6760
naive height: 248.3110
primes of bad reduction: 2, 5, 7, 13, 17, 23, 43, 33071, 35617, 18281328539821, 2179714251521392600543, 56649693004459884944464037627218223
regulator: 9877490249859092108552435.3971538358380200306145641639185705964072880531589261478977278
submitted by: apkorte
submitted at: 2026-11-01 03:30:18 UTC
last updated: 2026-11-01 03:30:18 UTC

(197139061458506480, -72806652265802572611931275)
(-148964521770896155, 12983114601195042157829410)
(4225429152427272648, -8681681964968644200100256381)
(807726469745904523/9, -354733459049978745884959442/27)
(1214438168147041995, -1331020315338433274989154390)
(-4140324183335861595/121, -51542203347313093426337312125/1331)
(-3805441200857614319/25, -180132727617080397651033494/125)
(387182861851378935/4, 123373270051976052491172175/8)
(122831411469218128, -27298391747680948879189771)
(321049674323470035/4, 90047594692514890278049805/8)
(689451710705525655/4, 450965737773297995670262135/8)
(63584709971296295, -12160700679351557340879990)
(75189969634981241, 10965674578601715520889685)
(-109366963470215180, -38709496776930362392960915)
(30982015720181803255/4, -172426465127349326763596959665/8)
(547383763691348835/4, 279244178724686920537603105/8)
(71799610621171774169/1024, 366950187155256949382937734867/32768)
(205615894631375190, 78672303113770312544627035)
(-140093646701465235, -23980926883868654477089150)
(152257998986447940, 43881639704610184191451535)
(465037198830289084/25, -3200613299393128046607118983/125)
(5816557536286428655/9, 13767596663715964405795945765/27)
(145609811836941555, 39940071129493889630764195)
(199780670641304485535/1849, 1595298711227744759889002563725/79507)

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