curve #2386

y² + xy = x³ − x² − 119180658744x + 15727915589300208

a-invariants: [1, -1, 0, -119180658744, 15727915589300208]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3028410
discriminant (Δ): 1479836157251574044321922080250000
Faltings height: 5.1928
naive height: 88.1253
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23
regulator: 4.828794103901928874622271539550714115328
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:20 UTC
last updated: 2026-09-26 19:58:20 UTC

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

(-223413, 176755674)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-12, q=23; A=(3q-p)(p+q)^3=107811, B=-(p+3q)(p-q)^3=2443875. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 19:58:20 UTC · history