curve #5491

y² + y = x³ + x² − 14516277353990560458013362010x + 616544414881881063063052103641597315899370

a-invariants: [0, 1, 1, -14516277353990560458013362010, 616544414881881063063052103641597315899370]
c-invariants: [696781312991546901984641376496, -532694374457949419174354966827751988785314840]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 100615537103103529082948543265639696294325163195433892104733813754908685877 ★ record for rank ≥ 23
discriminant (Δ): 31554951423452970457512130651620020348960790465170935376238447579212261925595324050837 ★ record for rank ≥ 23
Faltings height: 15.1442 ★ record for rank ≥ 23
naive height: 206.1488 ★ record for rank ≥ 23
primes of bad reduction: 3, 11, 13, 23, 47, 342838079880795773, 632838670731238608506562568687312618322420482797701
regulator: 10673918998607294133888.0317734231024911340295621052877619943189203101110333176507493
submitted by: Matej Jurasić
submitted at: 2026-10-22 11:56:48 UTC
last updated: 2026-10-22 11:56:48 UTC

(10578102570200, -681302718434162098346)
(-52435446069985, -1110649311194251606421)
(117173565245990, -724135226486676948455)
(104160129169547, 484350045039894368263)
(105239634514685, 504406290354285200029)
(89315649720605, -180305545459221109571)
(95321123363774, 314539962308599890505)
(128173933581716, -928250424852220391279)
(284089497756944, 4406879722711557398950)
(-137799608926210, 15552600292313657545)
(-46143122397064, -1090010737045135194647)
(-71121923331151, -1135434703207579587170)
(1250634401049011/25, 15588757187513962973816/125)
(251411582989784, -3585826710028907650391)
(13812807041693/4, 6021072108792758802209/8)
(51261172497479, 84394315712889199660)
(2136057044167739/25, -175897883318424273712/125)
(17829995737664, 602816359395942873670)
(-1897940180419591/25, 141478554702471288309302/125)
(323162963663686/9, 10160176996384425056195/27)
(130692566919170, 975538519718620292545)
(572833750088864, -13426464215367659045255)
(-85501779792832744/1369, 57297178776568917495246565/50653)

Specialization at T = -2/73 of a rank-16 fibration of X1152 (two neighbour steps from the one in curve#3856).

last edited by Matej Jurasić at 2026-10-22 11:56:48 UTC · history