curve #5611

y² = x³ + 6928864918417269

a-invariants: [0, 0, 0, 0, 6928864918417269]
c-invariants: [0, -5986539289512520416]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 2370823163341903594820345551524
discriminant (Δ): -20739961032914972647488382884731952
Faltings height: 5.2637
naive height: 86.4721
primes of bad reduction: 2, 3, 1753, 146391686599
regulator: 96024000335409228.5274389061821793801974653787850606656842749
submitted by: jesper-petersen
submitted at: 2026-10-23 22:41:58 UTC
last updated: 2026-10-23 22:41:58 UTC

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

(3564931117239555/27624766849, 437463973407587761365084/4591429623671743)
(1378210292013394903/1239060623161, 1622048406881648910186677554/1379236790519827091)
(188847890751468342588318271/207358302333122161, 2595184315602210062765333916887187285490/94423945375862483607463159)
(-2358417425505913961/22002807211225, 7790312509200471394998245962/103208897827801275875)
(28634076621379610025/164075297219344, 232556072740277568789463319061/2101671328238454532672)
(-4645140270603876642207/24374795176998436, 10621102813469303078570615450289/3805497688403485859604184)
(8757013835377001891305/33495773538472036, 965364620495914945629144907805717/6130346430325485551498216)
(-342937811109384361178694183/2025549151705520017984, 4153411855020753616473808831355685216867/91162070253072325450811165275648)
(-28900647762157044392998967/627643320763274724496, 1299627739623803799625811006417916429061/15724229262032528656043358539456)
(84065101488360268639475833/354729900310901947456, 950455540718024988943276664940192116429/6681080356961831057035506576896)
(3051645137651656799074080127/18934995061929944529, 168578057572086818128678706263503872403782/82394418736799303677104919833)

Commentary

Exact-rank-11 Mordell curve obtained by the rational 3-isogeny from y^2=x^3-256624626608047, discovered using the Burkhardt quartic construction with parameters (u,v,w)=(11,-8,2) and t=-645/722.

last edited by jesper-petersen at 2026-10-23 22:41:58 UTC · history