curve #6210

y² = x³ − 787324916162414812x + 265613994105200839858206100

a-invariants: [0, 0, 0, -787324916162414812, 265613994105200839858206100]
c-invariants: [37791595975795910976, -229490490906893525637490070400]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 1245212915429859025132950706418677615155698974680824
discriminant (Δ): 757089452581354287280834029502555990014664976605940992
Faltings height: 9.1435
naive height: 135.2359
primes of bad reduction: 2, 19, 11480353, 119663209, 5963265442184363921613680401905181
regulator: 1518295674386056.97358657607701356726445373073470240325395490936795330351
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-30 17:20:11 UTC
last updated: 2026-10-30 17:20:11 UTC

(-896583434, -15836263747502)
(102772650002/169, 7519868739189938/2197)
(1125919006, -28398419572462)
(1309446556, -38469429447662)
(1843294340953/2304, 1344502400773327651/110592)
(23133394904384129924/49721418289, 1426600108940920476618894374/11087031014336087)
(27888882729/64, -1175764868866859/512)
(2847404769/4, 64930080575119/8)
(29796596694/25, -3992805155085878/125)
(312229374, -7087057937006)
(37519853691970964/40436881, 4698721865251094304940214/257138126279)
(399478404, 3852875993354)
(431858888668449/399424, -6574419902734239104719/252435968)
(5556953225/16, 373522999189595/64)
(654205196, -5525539473022)
(657918750, 5692359745810)
(9661584913/16, -206118674268281/64)

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