curve #2529

y² + xy = x³ − x² − 39541104x + 3795068160

a-invariants: [1, -1, 0, -39541104, 3795068160]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 14490
discriminant (Δ): 3950448789976017960960000
Faltings height: 3.4092
naive height: 64.0922
primes of bad reduction: 2, 3, 5, 7, 23
regulator: 21.81255577826578952012083145922991155950
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:07:17 UTC
last updated: 2026-09-26 20:07:17 UTC

Witness: 1 independent point log in to add more points →

(-70572718389/17757796, 23593497514056903/74831352344)

Commentary

Exact computational full 2- and 3-torsion family at (p,q)=(-24,1); Velu quotient by rational order-3 subgroup. The mapped rank >=1 witness is non-torsion by the original exact 2-descent Kummer certificate and finite isogeny kernel. Conductor N=14490; local exponents {'2': 1, '3': 2, '5': 1, '7': 1, '23': 1}.

last edited by Natanael Wildner Fraga at 2026-09-26 20:07:17 UTC · history