curve #2643

y² + xy = x³ − 38630687530x + 2441391499124900

a-invariants: [1, 0, 0, -38630687530, 2441391499124900]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 25526670
discriminant (Δ): 1114686688288583278701121536000000
Faltings height: 5.0610
naive height: 84.7455
primes of bad reduction: 2, 3, 5, 13, 29, 37, 61
regulator: 10.9577057552565496430880654095952579932749
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:14:58 UTC
last updated: 2026-09-26 20:14:58 UTC

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

(-214540, 29339270)
(-192940, 52177670)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=8; A=(3q-p)(p+q)^3=-1487729, B=-(p+3q)(p-q)^3=-1184625. 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 20:14:59 UTC · history