curve #5643

y² = x³ − 378299145286766059274522169812658966292

a-invariants: [0, 0, 0, 0, -378299145286766059274522169812658966292]
c-invariants: [0, 326850461527765875213187154718137346876288]
rank (lower bound): ≥ 18
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1287992189922279616434391982992675411341005002930125590555730451717037930063376 ☆ record for Mordell curves, rank ≥ 18
discriminant (Δ): -61823625116269421588850815183648419744368240140646028346675061682417820643042048 ☆ record for Mordell curves, rank ≥ 18
Faltings height: 13.9894 ☆ record for Mordell curves, rank ≥ 18
naive height: 191.1806 ☆ record for Mordell curves, rank ≥ 18
primes of bad reduction: 2, 3, 401, 1201, 196375809688292829164869970064773
regulator: 4560850669596653123947.2839472155444997380181107198846937101502138684250155
submitted by: wgxli
submitted at: 2026-10-24 00:24:24 UTC
last updated: 2026-10-24 00:24:24 UTC

(8162915944381, 12869422621214378007)
(9151252868222, 19699656153903607766)
(15093639769381, 55320006312412878243)
(16184890929622, 62139715742645954334)
(20207654354198, 88732644802937807710)
(24275217505822, 118011656914353621366)
(28651708182557, 152126500237602721799)
(47633119169782, 328172445211044628926)
(31346091608417/4, 81171532865226985745/8)
(69290581685782/9, 238530510516497459930/27)
(110571417729313/4, 1152232292494470349647/8)
(131142139137382/9, 1406995598840489495990/27)
(510076907513393/4, 11518976032506035547863/8)
(181831203796486/25, 317625235879899954234/125)
(4943870608243438/81, 347327414315857630072630/729)
(4557248881734958/289, 292431326704347529169958/4913)
(118018360205717254/13689, 25949944832357170138878746/1601613)
(3416368473924489833/322624, 5212565388425722517353365323/183250432)

Isogenous to curve#5641

last edited by Maksym Voznyy at 2026-10-25 09:27:14 UTC · history