curve #763

y² + xy = x³ − x² − 7636625866x + 271218848904208

a-invariants: [1, -1, 0, -7636625866, 271218848904208]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 27751906366700157951398581202
discriminant (Δ): -3274724951270618638265032581836
Faltings height: 4.6074
naive height: 79.9910
primes of bad reduction: 2, 59, 7762277, 11379623, 2662525667609
regulator: 626215309.1609151752950619323807665746425606678245132892107547004
submitted by: Michael Rubinstein
submitted at: 2026-09-18 11:18:31 UTC
last updated: 2026-09-18 11:18:31 UTC

(35249, 6752242)
(-70538, 21457638)
(59793, -5356387)
(49586, 3778878)
(-44873, 22903433)
(209122, -88532640)
(60383, -5530791)
(-46584, 22955176)
(78673, -12583651)
(42624, -4833116)
(-74491, -20620218)
(181746, -69995312)
(88821, -17180459)

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

last edited by Michael Rubinstein at 2026-09-18 11:18:31 UTC · history