curve #2318

y² + xy = x³ − 721613468615x + 230068357838241225

a-invariants: [1, 0, 0, -721613468615, 230068357838241225]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2261048790
discriminant (Δ): 1182427153612105408903963708641000000
Faltings height: 5.7002
naive height: 93.5279
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 43, 103
regulator: 10.73536466544144421269848552910633177947
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:54:05 UTC
last updated: 2026-09-26 19:54:05 UTC

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

(2921695/4, 2432545805/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=30; A=(3q-p)(p+q)^3=506039, B=-(p+3q)(p-q)^3=6122039. 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 19:54:06 UTC · history