curve #3806

y² = x³ + x² − 2013725795072304864x + 647295898955199161707509876

a-invariants: [0, 1, 0, -2013725795072304864, 647295898955199161707509876]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 493791717782899536
discriminant (Δ): 341609384651553965423706917586466482403218680003404775424
Faltings height: 9.5473
naive height: 138.0532
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 23, 37, 47, 59, 97, 139
regulator: 3717.5748624021857273675389918769930274947213676994
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 11:15:54 UTC
last updated: 2026-10-02 11:15:54 UTC

(-1555220965, 4177616086644)
(-973237590, 41052250337856)
(-42626310, 27075009637104)
(1996312650, 67698618551424)
(-15446707039/16, 2632245940306983/64)
(15666687994/9, 1327316541072704/27)

(u,v) = (52687,29601) 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 11:15:54 UTC · history