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curve #1250

y² + xy + y = x³ + x² − 105079046100x + 13116959192846485

a-invariants: [1, 1, 1, -105079046100, 13116959192846485]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 43672360510
discriminant (Δ): -72640591228995082787392716800000
Faltings height: 5.0603
naive height: 87.7485
primes of bad reduction: 2, 5, 19, 79, 2909551
regulator: 246.9712513103996155999846855438082599443858048
submitted by: hdeping
submitted at: 2026-09-24 16:26:19 UTC
last updated: 2026-09-24 16:26:19 UTC

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

(2960333/16, 185584387/64)
(183293, 3744833)
(26385965/49, 115045012055/343)
(2756197/9, 2649360091/27)

Commentary

Found by a Mestre-Nagao sieve over the Tate normal form family y^2+(t+1)xy+ty=x^3+tx^2 with torsion Z/5Z, at t=10112/760.

last edited by hdeping at 2026-09-27 08:28:22 UTC · history

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