curve #2501

y² + xy = x³ − 308191351x + 2079634736105

a-invariants: [1, 0, 0, -308191351, 2079634736105]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 881790
discriminant (Δ): 5051998285778491505640000
Faltings height: 3.6388
naive height: 70.2523
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19
regulator: 3.377125221154720408890319929615723290201
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:05:31 UTC
last updated: 2026-09-26 20:05:31 UTC

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

(-9214, 2038589)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-19, q=2; A=(3q-p)(p+q)^3=-122825, B=-(p+3q)(p-q)^3=-120393. 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 20:05:31 UTC · history