curve #2303

y² + xy = x³ − 1248257599600x − 505258705663840000

a-invariants: [1, 0, 0, -1248257599600, -505258705663840000]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 20930910
discriminant (Δ): 14194346213134336352363321757696000000
Faltings height: 5.8784
naive height: 95.1719
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 41
regulator: 4.667474103280524202821019743216159450975
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:53:12 UTC
last updated: 2026-09-26 19:53:12 UTC

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

(-2075005/4, 416155735/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-1, q=40; A=(3q-p)(p+q)^3=7177599, B=-(p+3q)(p-q)^3=8201599. 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 19:53:12 UTC · history