curve #3885

y² + xy + y = x³ − x² − 3170616465080385830225026926173x + 2550703764273194632584660736295191518442666981

a-invariants: [1, -1, 1, -3170616465080385830225026926173, 2550703764273194632584660736295191518442666981]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 2969649879571017464627765439908785114949621389797758650975395666839253213929730
discriminant (Δ): -770720283271803877030248489206513909481944651111669747834975040005698845296174700412536115200
Faltings height: 16.5441
naive height: 222.6285
primes of bad reduction: 2, 3, 5, 7, 19, 248091050924897031297223512105997085626534786115100973347986271248057912609
regulator: 14128980335236806797741.86497480698949654966854937200813271694757866792792088746039
submitted by: 7fff-zip
submitted at: 2026-10-04 14:06:14 UTC
last updated: 2026-10-04 14:06:14 UTC

(3920075766813895/9, -955483771619612113281736/27)
(-86571087822095, -53146389007096247798638)
(7929966359310589039/7225, -12173473544694259656378597808/614125)
(706801130757840071/361, 425495551446392007520441208/6859)
(-845320280706785, -68020972182713865745048)
(-3482722969928332085/2116, -5600418809465764750765571653/97336)
(1971685517762735, -62962362522496372484888)
(1601574957849263, 39759669965047522488296)
(81708806748807619615/7569, -729231813899042808280999377064/658503)
(160931347504785091/121, -34872319112739381626940968/1331)
(196774797883146395647/25281, -2694744207446643286072078722536/4019679)
(1141859489054669287/2209, 3364075026727382692982484088/103823)
(413353141618042708711/249001, 5361580117530869189714323882424/124251499)
(-75715451660578265/121, 87174825800161225448215912/1331)
(7343150618062537, -612555908414173435490404)
(957714530150989267/2916, -6188940942099448216287314701/157464)
(168896715881545096471085/232959169, 89463855046214835550759977348314404/3555655796447)
(-234712192407480545/1681, 3769092727962838256094544552/68921)
(-10533361714736682017/6241, -27425812241738035859096766040/493039)
(104900356344654337/169, 62982044829260316653663570/2197)
(30814571477557111/25, -2837446973704870406702456/125)
(18928383780662359/9, 1944224338949421839891192/27)

X1008, t=-51/26

last edited by 7fff-zip at 2026-10-04 14:06:14 UTC · history