curve #5416

y² + y = x³ − 270331067572327

a-invariants: [0, 0, 1, 0, -270331067572327]
c-invariants: [0, 233566042382490312]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 260909742090503810360561327163
discriminant (Δ): -31570078792950961053627920586723
Faltings height: 4.7230
naive height: 79.9845
primes of bad reduction: 3, 11, 2978854739089
regulator: 348062853335878.4294382824592604075111038628032057905010267
submitted by: The Wren
submitted at: 2026-10-21 22:27:37 UTC
last updated: 2026-10-21 22:27:37 UTC

Witness: 10 independent points log in to add more points →

(3068651623057/8433216, -5360429119701074887/24490059264)
(821885381304769/12421102500, -6092973201392830250603/1384331873625000)
(374618115486709273/4430738724624, 170468605013944125923862371/9326403725100245568)
(399681500548063057/3846878131716, 220131451708737877327088987/7545059036128649736)
(6193390334728415569873/94001547488371524, 114117630541258123745394810544709/28820565946855852423058232)
(137903907521847553/1850845969764, 30143020365071084172194389/2517998206333191912)
(61341701101771735753/179292314240064, 478809739500105004047431309179/2400725522012970880512)
(1476143835388739137/122839034256, 1793465314812295316681545153/43053116082179904)
(175898326955359633/268894404, 73772170799038240826342179/4409330436792)
(318629506058416177/4472692035876, -90336145846242774053658437/9459180096681219624)

Commentary

Rational 3-isogeny partner of curve #5414: https://elliptic-rank.icarm.cloud/curve/5414 The source curve was submitted by Jesper Petersen and obtained through Mestre’s polynomial cube-completion construction from the integer sextuple (-45,-13,-1,9,11,39). The ten source points were transported through the exact degree-3 isogeny and checked exactly on this minimal target model. Rank ≥10 is preserved under the rational isogeny. Rational torsion is trivial.

last edited by The Wren at 2026-10-21 22:27:37 UTC · history