curve #5641

y² = x³ + 10214076922742683600412098584941792089884

a-invariants: [0, 0, 0, 0, 10214076922742683600412098584941792089884]
c-invariants: [0, -8824962461249678630756053177389708365659776]
rank (lower bound): ≥ 18
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1287992189922279616434391982992675411341005002930125590555730451717037930063376 ☆ record for Mordell curves, rank ≥ 18
discriminant (Δ): -45069422709760408338272244268879697993644447062530954664726119966482591248777652992
Faltings height: 14.5387
naive height: 197.7723
primes of bad reduction: 2, 3, 401, 1201, 196375809688292829164869970064773
regulator: 4560850669596653123947.2839472155444997380181107198846937101502138684250155
submitted by: wgxli
submitted at: 2026-10-24 00:23:59 UTC
last updated: 2026-10-24 00:23:59 UTC

(-21652808368755, 7892100391708490247)
(-9854441545755, 96213886342323047253)
(7225262160306, 102913883877020459850)
(-3849056858622, 100782201933718648506)
(69637522047090, 589841669725718453622)
(123572700422245, 1377387180706732352747)
(19878763092649/4, 813361124524639254805/8)
(56194807750737/4, 911677606052418486873/8)
(385016132690521/16, 9945383762345233600675/64)
(-516913375504451/25, 4634219309061454640657/125)
(1308681389864749/25, 48999022258462444687193/125)
(42299376732650005/9, 8699633835814451608106669/27)
(76053773064421753/16, 20973995349582934818387379/64)
(9142824626056410/289, 1005387016864680119242386/4913)
(19240938228165529/400, 2788720124181945673670333/8000)
(-29039195056474398/4489, 29991012836170762212096402/300763)
(-486125058851751950/52441, 1165397594079687063294234158/12008989)
(22873662331470946698/58081, 109405679363324934633653856606/13997521)

Specialization at (a, b, c, d, T) = (-7/8, -5/8, -1/4, 3/16, 2822744/6978815) of the rank-4 universal family described in curve#5569.

last edited by Maksym Voznyy at 2026-10-25 09:25:35 UTC · history