curve #3808

y² + xy + y = x³ + x² − 1590515024185000595x + 765615224263330609470418232

a-invariants: [1, 1, 1, -1590515024185000595, 765615224263330609470418232]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1399247370885655005
discriminant (Δ): 4285524671661723608766978246273261126127899703749950625
Faltings height: 9.3029
naive height: 137.3454
primes of bad reduction: 3, 5, 11, 13, 17, 43, 97, 101, 107, 127, 6703
regulator: 280262.90701774347173738399540763074659716713375606
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 12:04:59 UTC
last updated: 2026-10-02 12:04:59 UTC

(3302115657, 177536270271511)
(49700546736, 11076492682686439)
(266966902563/4, 137913983890909433/8)
(-5331500431685/5476, 15114850818814032697/405224)
(28806521901/16, 3912851729429011/64)
(701573209912/841, 107205043312834384/24389)

(u,v) = (94588,20855) 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 12:04:59 UTC · history