curve #3801

y² = x³ + x² − 746073122124619920x + 88653323868322644159869268

a-invariants: [0, 1, 0, -746073122124619920, 88653323868322644159869268]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 74561461260096720
discriminant (Δ): 23182847916404503906718760019211725831688710154672640000
Faltings height: 9.3162
naive height: 135.0744
primes of bad reduction: 2, 3, 5, 7, 13, 43, 47, 79, 107, 337, 593
regulator: 97214.498744627196888548219714852363052750637439192
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 07:34:40 UTC
last updated: 2026-10-02 07:34:40 UTC

(112554426, 2470908229440)
(1668653691, 59075575093080)
(206044954/9, 228441081831200/27)
(9118935069/4, 809385179860845/8)
(107322631989/4, 35140894029744615/8)
(20718785609196/121, 94306347078088926690/1331)

(u,v) = (41409,25991) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 6.

last edited by Daniel Błażewicz at 2026-10-02 07:34:40 UTC · history