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curve #3747

y² = x³ + x² − 39905320x + 96935961668

a-invariants: [0, 1, 0, -39905320, 96935961668]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 29636880
discriminant (Δ): 6546214887704069760000
Faltings height: 3.1089
naive height: 64.1197
primes of bad reduction: 2, 3, 5, 7, 13, 23, 59
regulator: 10.178640078643147585683605996565809701586838
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 06:31:41 UTC
last updated: 2026-10-01 06:31:41 UTC

Witness: 3 independent points log in to add more points →

(-6409, 299130)
(74126, 20110740)
(-7826/9, 9771580/27)

Commentary

(u,v) = (105,13) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 3.

last edited by Daniel Błażewicz at 2026-10-01 06:31:41 UTC · history

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