curve #2477

y² + xy = x³ − 2211087885x + 23468731830225

a-invariants: [1, 0, 0, -2211087885, 23468731830225]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 36606570
discriminant (Δ): 453886477750563042153969000000
Faltings height: 4.3900
naive height: 76.1639
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 53
regulator: 2.252289952309771551959963814776936183987
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:04:03 UTC
last updated: 2026-09-26 20:04:03 UTC

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

(-49200, 3652185)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=10; A=(3q-p)(p+q)^3=-116441, B=-(p+3q)(p-q)^3=251559. 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 20:04:03 UTC · history