curve #4303

y² + xy = x³ + x² + 2129783152978x + 306083762929291740

a-invariants: [1, 1, 0, 2129783152978, 306083762929291740]
c-invariants: [-102229591342919, -264455604448972991405]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 671251925040138068164062
discriminant (Δ): -658754001012993194397931407867303761928
Faltings height: 6.1378
naive height: 96.7747
primes of bad reduction: 2, 3, 7, 23, 31, 43, 107, 139, 193, 23041, 7881721
regulator: 2993864642.293873953323916089660794390928364954786075938500
submitted by: The Wren
submitted at: 2026-10-16 19:13:05 UTC
last updated: 2026-10-16 19:13:05 UTC

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

(5906779, 14794817742)
(3665991, -7576984206)
(54331, -649609641)
(-8039, 537555800)
(476221, 1194890324)
(-284289/4, -3142771893/8)
(2780029, 5262883604)
(-1249619/81, 381059359255/729)
(-4738121/36, -33093466663/216)
(260229, -937113396)

Commentary

Obtained by a rational 2-isogeny from curve#4095, submitted by Michael Rubinstein and sourced from his elliptic-curves-by-rank repository. This isogenous curve has the same rank and conductor. The ten supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 19:13:06 UTC · history