curve #5731

y² + y = x³ − 372755707785

a-invariants: [0, 0, 1, 0, -372755707785]
c-invariants: [0, 322060931526024]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 60025025240399490517007667
discriminant (Δ): -60025025240399490517007667
Faltings height: 3.6253
naive height: 66.8115
primes of bad reduction: 3, 1491022831139
regulator: 605896902094.92574158969530798146174687156184039627669169
submitted by: jesper-petersen
submitted at: 2026-10-24 17:18:36 UTC
last updated: 2026-10-24 17:18:36 UTC

Witness: 9 independent points log in to add more points →

(36281766113065/2258720676, 208481651899165166615/107347958847576)
(496992571041/126736, 350368330829833297/45118016)
(497009490297/31684, -350386223602931929/5639752)
(497274003297/861184, -350665639903437679/799178752)
(503168779041/6990736, -356741273440773487/18483505984)
(527707763745/20394256, -379198907521670511/92100460096)
(42425819872665/4019306404, -228387718774731412295/254815987400792)
(2248780379865/302272996, 1037883110558647815/5255318308456)
(4662627218985/538518436, 6569022345479416215/12496858825816)

Commentary

Constructed by specializing the Burkhardt rank-four Mordell family with parameters (u,v,w) = (7,-2,3) and t = 115/152. PARI/GP 2.17.4 computation returned matching rank bounds [9,9], together with nine rational points on the original curve.

last edited by jesper-petersen at 2026-10-24 17:18:36 UTC · history