curve #1762

y² + xy = x³ + x² − 134726750x + 601046062500

a-invariants: [1, 1, 0, -134726750, 601046062500]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 4309549350
discriminant (Δ): 417874851001922006250000
Faltings height: 3.4316
naive height: 67.7699
primes of bad reduction: 2, 3, 5, 29, 61, 109, 149
regulator: 11038.5988620526396890413523381325425988661179281
submitted by: jesper-petersen
submitted at: 2026-09-25 12:36:32 UTC
last updated: 2026-09-25 12:36:32 UTC

Witness: 5 independent points log in to add more points →

(7400, 93050)
(107624, -35163874)
(510344/49, 194587154/343)
(1333725/169, 368012100/2197)
(527725/9, -377156275/27)

Commentary

"2-isogenous to curve#1685 (Michael Rubinstein). The five witnesses are the images of curve #1685's certified independent points under the rational 2-isogeny."

last edited by jesper-petersen at 2026-09-25 12:36:32 UTC · history