curve #2497

y² + xy = x³ − 335944840x + 1934592833600

a-invariants: [1, 0, 0, -335944840, 1934592833600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 146370
discriminant (Δ): 809648781931584000000000000
Faltings height: 3.8803
naive height: 70.5110
primes of bad reduction: 2, 3, 5, 7, 17, 41
regulator: 2.401259260050151923957967263138789341971
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:05:16 UTC
last updated: 2026-09-26 20:05:16 UTC

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

(-19360, 1097000)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=8; A=(3q-p)(p+q)^3=-29889, B=-(p+3q)(p-q)^3=109375. 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 20:05:16 UTC · history