curve #2297

y² + xy = x³ − 1614836008220x + 779256263039024400

a-invariants: [1, 0, 0, -1614836008220, 779256263039024400]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 952220490
discriminant (Δ): 7176110317928259949220037267456000000
Faltings height: 5.8734
naive height: 95.9444
primes of bad reduction: 2, 3, 5, 13, 17, 31, 41, 113
regulator: 3.613159474133285805431677287745670265409
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:52:48 UTC
last updated: 2026-09-26 19:52:48 UTC

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

(809320, 49002100)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-41, q=24; A=(3q-p)(p+q)^3=-555169, B=-(p+3q)(p-q)^3=8513375. 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 19:52:48 UTC · history