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curve #1779

y² + xy = x³ − 3851007361865880x + 91983425752602030975552

a-invariants: [1, 0, 0, -3851007361865880, 91983425752602030975552]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 302411130
discriminant (Δ): 931070454323424230940837829622303293440000
Faltings height: 7.4608
naive height: 119.2749
primes of bad reduction: 2, 3, 5, 7, 17, 23, 29, 127
regulator: 29.9597410164076365742877022965090208598204
submitted by: hdeping
submitted at: 2026-09-25 14:35:42 UTC
last updated: 2026-09-25 14:35:42 UTC

Witness: 2 independent points log in to add more points →

(26320944, 94094324328)
(615030430584/17161, -10546168471752/2248091)

Commentary

Specialization t=9/8 of the universal torsion Z/2xZ/8 family y^2=x(x+16t^4)(x+(t^2-1)^4).

last edited by hdeping at 2026-09-27 08:34:12 UTC · history

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