curve #5599

y² + y = x³ + 885531090318187255

a-invariants: [0, 0, 1, 0, 885531090318187255]
c-invariants: [0, -765098862034913788536]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 41735582127674531636546296520307
discriminant (Δ): -338759414749490766062050616142324377907
Faltings height: 6.0721
naive height: 96.1731
primes of bad reduction: 3, 7, 11, 37, 292343, 1492747
regulator: 285504263717166.409676058624072689358403493382914503587742004
submitted by: jesper-petersen
submitted at: 2026-10-23 21:43:11 UTC
last updated: 2026-10-23 21:43:11 UTC

Witness: 11 independent points log in to add more points →

(-12030129572166527/12738733956, 299174896090611183126853/1437769946677896)
(-12997314559015/14167696, 17961811078211317245/53327207744)
(-8687562288719/9511056, 10305496553577190793/29332096704)
(-124808520646207/203176516, 2341585687654016539899/2896078059064)
(-2126307780847/15413476, 56860159229029946613/60513306776)
(20424785486345/34550884, 212237827723347975335/203090096152)
(753837492137/964324, 1105657934184096689/946966168)
(457414373754545/311663716, 11068502055742396439845/5502111242264)
(2724215402651737/876041604, 144266117028253501948937/25929079395192)
(20951894954040185/3147434404, 3037287140732142338197215/176577364933208)
(683820447251489/5330460100, 366662116546255378205013/389176891901000)

Commentary

The rational 3-isogenous partner of our accepted rank-11 Mordell curve obtained from the Burkhardt quartic with parameters (u,v,w) = (3,-2,-6), specialized at t = -169/16.

last edited by jesper-petersen at 2026-10-23 21:43:11 UTC · history