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curve #3760

y² = x³ − x² − 11143738499300x − 10896754631522061948

a-invariants: [0, -1, 0, -11143738499300, -10896754631522061948]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 34669645505880
discriminant (Δ): 37271762456709170486230337215584300960000
Faltings height: 6.4957
naive height: 101.7393
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23, 31, 47, 71, 83
regulator: 558.960210470227501156768378563946564967344403851
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 17:54:50 UTC
last updated: 2026-10-01 17:54:50 UTC

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

(-2628431, 484641740)
(-2528818, 1054578336)
(19555874, 85146775560)
(30415324, 166694729390)
(259900814, 4189628327280)

Commentary

(u,v) = (2530,2201) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5.

last edited by Daniel Błażewicz at 2026-10-01 17:54:50 UTC · history

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