curve #5

y² = x³ + x² − 18478018087690013395692891145x + 966788754934919721471057668405679651084743

a-invariants: [0, 1, 0, -18478018087690013395692891145, 966788754934919721471057668405679651084743]
c-invariants: [886944868209120642993258774976, -835305484263775961020203080226365178089867776]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 142982366755806522511963024785618677537647778562138917247360
discriminant (Δ): -734320078819007341646140177726248140770988611740198639931331272725700464000000000
Faltings height: 14.8061
naive height: 206.8727
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 831851, 276884796725521287156064626403852388034812821
regulator: 4806705005919007.18083185494710935314841121112705422150723975823444038217
submitted by: David Renshaw
submitted at: 2026-05-27 22:11:46 UTC
last updated: 2026-07-01 22:36:40 UTC

(987132393978079331954/12581209, 44155864801840452651790531875/44625548323)
(6360438106451911/81, 832408927123396980500/729)
(13270945713669554/169, 2555271033060881176965/2197)
(857729078027047559/10609, 39912099554742671720961420/1092727)
(79430124839906, 14615920705150940175)
(4607314783851323, -312597047325749802318252)
(2573692194283109/4, -127862522511653550016935/8)
(17056161852252119/49, -2078193005890922295589500/343)
(4301027702330981171/52441, -656366039306811393976716300/12008989)
(81650469905306, -48961061265151525875)
(14515046737185390509/187489, 1323774083443035484317172500/81182737)
(951024572107238604431/12243001, 528074563286919141440933947500/42838260499)
(63250318746985598981/811801, 6402633724575591190797301500/731432701)
(383087327491229/4, -2199020909677353716955/8)
(1738525538929581791/22201, 9310903033909158740238180/3307949)
(443811832334711, -8954505736358951228460)
(4025605174011254909/27889, -5324653812843602019420280500/4657463)

Found by Nagao (1992). A historical rank ≥ 17 record, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:31:37 UTC · history