curve #3878

y² + y = x³ − 69573490077x + 7061376552317536

a-invariants: [0, 0, 1, -69573490077, 7061376552317536]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 50809100449337709791877402759
discriminant (Δ): 12346611409189063479426208870437
Faltings height: 4.9389
naive height: 86.5106
primes of bad reduction: 3, 211, 1230223, 21748669769673237467
regulator: 252839382276.4252146195970826146096661038887449940638602441278117
submitted by: Michael Rubinstein
submitted at: 2026-10-04 12:43:55 UTC
last updated: 2026-10-04 12:43:55 UTC

(-131756, 118071436)
(155146, 1317469)
(156727, 2659459)
(179261, 18709004)
(198508, 32753236)
(212140, 43000852)
(1274863, 1410804211)
(3904015, 7696612147)
(3808681/49, 15804685084/343)
(3864179/25, 75505908/125)
(34977961/196, 49760617775/2744)
(40570441/256, 16244872645/4096)
(271425706/1849, 270597222391/79507)

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

last edited by Michael Rubinstein at 2026-10-04 12:43:55 UTC · history