curve #5502

y² = x³ − 347813836592077294701537777075

a-invariants: [0, 0, 0, 0, -347813836592077294701537777075]
c-invariants: [0, 300511154815554782622128639392800]
rank (lower bound): ≥ 13
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 13509068122816118157587695955324550113332646320712100
discriminant (Δ): -52260968847556906491388686445942055973001896233759594880030000
Faltings height: 10.5215
naive height: 149.5661
primes of bad reduction: 2, 3, 5, 7, 19, 15643, 23173, 80359549469599
regulator: 4823598239037211.190562810041235364769669066268275589376139858884
submitted by: jesper-petersen
submitted at: 2026-10-22 15:27:40 UTC
last updated: 2026-10-22 15:27:40 UTC

(47000025503740911/1352569, -10147044981017667008797434/1573037747)
(11514245758929291/231361, -1233785470943395483919064/111284641)
(1245259657517799/160801, 22019074467809464471482/64481201)
(29380143807155631/2948089, -4055719975384264824852054/5061868813)
(332954261234931/1849, -6075246880131961783104/79507)
(3813995994595593499/66699889, 7441594738471577716950324232/544737993463)
(277137217084740686751/8499918025, 4590418199434954899185923155126/783649942314875)
(8705768115764525911/614593681, 24063862396918871674617817634/15236391945671)
(195912306684944087371/9156001969, -2693039694607588215790577379556/876110360407703)
(56052645560155004299/6000826225, 317730901850253182881659517532/464854003519625)
(7082533819, 86384289452572)
(7253896251, 184062513099276)
(2667706904682680345002189662900573199/273811867831694667626439289, 3441667302157870852359108995390611946365320085933332382/4530836617554214149801931888748583425587)

Mordell curve of rank at least 13, discovered using Mestre's polynomial cube-completion construction with sextuple (-34,-33,-10,14,25,38).

last edited by jesper-petersen at 2026-10-22 15:27:40 UTC · history