curve #2635

y² + xy = x³ − 2137879486x + 25009902667316

a-invariants: [1, 0, 0, -2137879486, 25009902667316]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 356730
discriminant (Δ): 355141540928868152378906250000
Faltings height: 4.3732
naive height: 76.0628
primes of bad reduction: 2, 3, 5, 11, 23, 47
regulator: 103.375471794065322458431197330766269688652
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:14:17 UTC
last updated: 2026-09-26 20:14:17 UTC

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

(2770294/49, 3149913346/343)
(18339764/169, -72017958466/2197)

Commentary

3-isogenous to S-1179; original source https://elliptic-rank.icarm.cloud/curve/1179. Rational 3-torsion kernel with x=25484; independent point witnesses transported by explicit Vélu map.

last edited by Natanael Wildner Fraga at 2026-09-26 20:14:17 UTC · history