curve #2281

y² + xy + y = x³ − 2974001501398x + 1686441941917711256

a-invariants: [1, 0, 1, -2974001501398, 1686441941917711256]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 87717630
discriminant (Δ): 454817104728198841795673573472656250000
Faltings height: 6.1408
naive height: 97.7764
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 127
regulator: 5.762305545586032285147944813002522381733
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:46 UTC
last updated: 2026-09-26 19:51:46 UTC

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

(-1953350, 207260252)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-52, q=25; A=(3q-p)(p+q)^3=-2499741, B=-(p+3q)(p-q)^3=10500259. 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 19:51:46 UTC · history