curve #2358

y² + xy = x³ − 7919096288985x + 8577514598574447225

a-invariants: [1, 0, 0, -7919096288985, 8577514598574447225]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1940819790
discriminant (Δ): 7278209249746750583314556601000000
Faltings height: 5.9118
naive height: 100.7145
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 31, 71
regulator: 2.509598745463824716901442373394368502011
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:37 UTC
last updated: 2026-09-26 19:56:37 UTC

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

(1531242, 203608107)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=34; A=(3q-p)(p+q)^3=3591, B=-(p+3q)(p-q)^3=19498375. 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 19:56:37 UTC · history