curve #2626

y² + xy = x³ − x² − 706464741465x + 228525329480211225

a-invariants: [1, -1, 0, -706464741465, 228525329480211225]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 109819710
discriminant (Δ): 5179079606124995160871525788644100
Faltings height: 5.4887
naive height: 93.4642
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 53
regulator: 26.0840665933376014431768592564593253814323
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:34 UTC
last updated: 2026-09-26 20:13:34 UTC

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

(-868770, 432367425)
(221836, 287504795)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-30, q=23; A=(3q-p)(p+q)^3=-33957, B=-(p+3q)(p-q)^3=5806203. 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 20:13:34 UTC · history