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curve #3876

y² + xy + y = x³ + x² − 32658450x + 71822280750

a-invariants: [1, 1, 1, -32658450, 71822280750]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/4ℤ
conductor (N): 7877415
discriminant (Δ): 1567605585 ☆ record for ℤ/4ℤ torsion, rank ≥ 3
Faltings height: 2.5013
naive height: 63.5184
primes of bad reduction: 3, 5, 7, 13, 29, 199
regulator: 502.82766162753825171309142237540412829107653
submitted by: jesper-petersen
submitted at: 2026-10-04 07:35:13 UTC
last updated: 2026-10-04 07:35:13 UTC

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

(83844/25, 473218/125)
(2062899/625, -28341282/15625)
(11220, -1062975)

Commentary

2-isogenous to curve #3741.

last edited by jesper-petersen at 2026-10-04 07:35:13 UTC · history

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