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curve #3751

y² = x³ + x² − 25158134820x + 762554918469600

a-invariants: [0, 1, 0, -25158134820, 762554918469600]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 150218348280
discriminant (Δ): 767887256560051793397847174560000
Faltings height: 5.0061
naive height: 83.4589
primes of bad reduction: 2, 3, 5, 7, 11, 13, 43, 127, 229
regulator: 109.4906765339017256891101329388692966295027869
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 07:44:59 UTC
last updated: 2026-10-01 07:44:59 UTC

Witness: 4 independent points log in to add more points →

(-21780, 36057840)
(-3762, 29277066)
(-1247826/25, 5439909618/125)
(664085/4, 272687415/8)

Commentary

(u,v) = (559,330) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 4.

last edited by Daniel Błażewicz at 2026-10-01 07:44:59 UTC · history

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