curve #2503

y² + xy = x³ − 226463430x + 1303007148900

a-invariants: [1, 0, 0, -226463430, 1303007148900]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1111110
discriminant (Δ): 9834476331017834496000000
Faltings height: 3.6250
naive height: 69.3279
primes of bad reduction: 2, 3, 5, 7, 11, 13, 37
regulator: 1.546996200522784560357742642493990056285
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:05:39 UTC
last updated: 2026-09-26 20:05:39 UTC

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

(-14790, 1197870)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=8; A=(3q-p)(p+q)^3=-4625, B=-(p+3q)(p-q)^3=101871. 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 20:05:39 UTC · history