curve #2241

y² + xy = x³ − 15193716871190x + 18109160049858584100

a-invariants: [1, 0, 0, -15193716871190, 18109160049858584100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3425022510
discriminant (Δ): 82806285030662333416008295519617024000000
Faltings height: 6.5658
naive height: 102.6693
primes of bad reduction: 2, 3, 5, 7, 13, 61, 131, 157
regulator: 3.155818330594945098159137386892718416419
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:49:12 UTC
last updated: 2026-09-26 19:49:12 UTC

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

(3156142, 1261235572)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=48; A=(3q-p)(p+q)^3=6731375, B=-(p+3q)(p-q)^3=29734511. 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 19:49:13 UTC · history