curve #4095

y² + xy = x³ + x² − 551445732182x + 38891260836442260

a-invariants: [1, 1, 0, -551445732182, 38891260836442260]
c-invariants: [26469395144761, -33602247883149698285]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 671251925040138068164062
discriminant (Δ): 10078768283566490372233622647727871552
Faltings height: 5.7912
naive height: 92.7210
primes of bad reduction: 2, 3, 7, 23, 31, 43, 107, 139, 193, 23041, 7881721
regulator: 2923695.939740111282542886806309369522390981401158277283692
submitted by: Michael Rubinstein
submitted at: 2026-10-09 14:50:40 UTC
last updated: 2026-10-09 14:50:40 UTC

(-19309, 222567350)
(-72268, -279902638)
(-669581, -328192713)
(764929, 253876544)
(1033477, 756329852)
(735788, -177818230)
(2965316, 4946042834)
(-705691, 277134719)
(-769492, -86764918)
(-572659, -408229516)

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-09 14:50:40 UTC · history