curve #5417

y² = x³ − 72569374790987

a-invariants: [0, 0, 0, 0, -72569374790987]
c-invariants: [0, 62699939819412768]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 5451618715945823931151788
discriminant (Δ): -2275047716063647459652539561008
Faltings height: 4.5038
naive height: 77.3543
primes of bad reduction: 2, 3, 17, 19, 383, 1816141
regulator: 59222328869.399750729123761032823035043987206106457023710
submitted by: The Wren
submitted at: 2026-10-21 22:30:15 UTC
last updated: 2026-10-21 22:30:15 UTC

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

(50468215767/1194649, 2194263601190950/1305751357)
(71496940611/1050625, 16772618448366484/1076890625)
(861321879/7225, 24731032956242/614125)
(230138001/400, 3490597292999/8000)
(231860883, -3530540747120)
(83704671993/4096, -24217234464281485/262144)
(69609200289/348100, -18281855533176337/205379000)
(189758423217/4545424, -4207399337662825/9690843968)
(411625388361/9424900, 94808818435028891/28934443000)

Commentary

Rational 3-isogeny partner of curve #5413: https://elliptic-rank.icarm.cloud/curve/5413 The source curve was submitted by Jesper Petersen and found through Mestre’s polynomial cube-completion construction from the integer sextuple (-49,-31,-5,7,29,49). The nine source points were transported through the exact degree-3 isogeny and checked exactly on this minimal target model. Rank ≥9 is preserved under the rational isogeny. Rational torsion is trivial.

last edited by The Wren at 2026-10-21 22:30:15 UTC · history