curve #5960

y² = x³ − 2663039488785316x

a-invariants: [0, 0, 0, -2663039488785316, 0]
c-invariants: [127825895461695168, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
families: y² = x³ + ax (quartic twists); y² = x³ − n²x (congruent-number curves)
conductor (N): 42608631820565056 ☆ record for congruent-number curves, rank ≥ 5
discriminant (Δ): 1208684055794893164790451414318656388011291807744
Faltings height: 7.9156
naive height: 118.1683
primes of bad reduction: 2, 19, 31, 71, 617
regulator: 112839.323998191928974994469790667757228819915673
submitted by: Lewis Combes
submitted at: 2026-10-26 22:31:21 UTC
last updated: 2026-10-26 22:31:21 UTC

(27450326876129/30976, 143576602964400908625/5451776)
(66115288038353/614656, -471684765010481618457/481890304)
(7459158681225/139876, 5135639657527248645/52313624)
(7143396609989/112225, -11177118401587473987/37595375)
(-409975/4, 132168093435/8)

Found by brute force searching of squarefree n (carried out by Claude code, Opus 5.5)

last edited by Lewis Combes at 2026-10-26 22:32:52 UTC · history