curve #4240

y² = x³ − 37758892927x + 2824446134548930

a-invariants: [0, 0, 0, -37758892927, 2824446134548930]
c-invariants: [1812426860496, -2440321460250275520]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 27921029408976004366433952184
discriminant (Δ): -893472941087232139725886469888
Faltings height: 4.7603
naive height: 84.6773
primes of bad reduction: 2, 26863597, 129920377979240849459
regulator: 772337176.7878516259259592001954246619151522945094951583372393481
submitted by: Michael Rubinstein
submitted at: 2026-10-15 17:34:11 UTC
last updated: 2026-10-15 17:34:11 UTC

(111003, -915224)
(103265, 5143630)
(107409, 2818846)
(118187, -3562528)
(1015201/9, -18942578/27)
(91711, 11528792)
(81617, -16922078)
(49215, 32944600)
(110693, -1056274)
(112173, -605174)
(112283, -607576)
(193933, 52873174)
(455809/4, 9527831/8)

From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-15 17:34:11 UTC · history