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curve #3761

y² + xy + y = x³ + x² − 4813456386275x + 3985595334667340417

a-invariants: [1, 1, 1, -4813456386275, 3985595334667340417]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 4743333870
discriminant (Δ): 275267760282038614743975330201600000000
Faltings height: 6.1633
naive height: 99.2209
primes of bad reduction: 2, 3, 5, 11, 31, 41, 43, 263
regulator: 66.78282975079734102631761735268176762076916917
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 19:30:04 UTC
last updated: 2026-10-01 19:30:04 UTC

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

(1699067, 843028046)
(2130387, 1842827806)
(20245827, 90572252926)
(4900738043/4489, 53484368568778/300763)

Commentary

(u,v) = (3968,1075) 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 19:30:04 UTC · history

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