curve #2283

y² + xy + y = x³ − 2512896255783x + 1479543776721230806

a-invariants: [1, 0, 1, -2512896255783, 1479543776721230806]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 109394670
discriminant (Δ): 69885698868851003385720227938476562500
Faltings height: 6.0282
naive height: 97.2710
primes of bad reduction: 2, 3, 5, 7, 11, 23, 29, 71
regulator: 4.877789018871806746599823616624071036304
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:56 UTC
last updated: 2026-09-26 19:51:56 UTC

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

(726467, 193037358)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-46, q=25; A=(3q-p)(p+q)^3=-1120581, B=-(p+3q)(p-q)^3=10379419. 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 19:51:56 UTC · history