curve #2368

y² + xy + y = x³ − 158984412254x + 11854925028855056

a-invariants: [1, 0, 1, -158984412254, 11854925028855056]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 223092870
discriminant (Δ): 196470710648252108096051355186254400
Faltings height: 5.4679
naive height: 88.9898
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23
regulator: 7.321350379688373081827001987554927699302
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:14 UTC
last updated: 2026-09-26 19:57:14 UTC

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

(-389892, 120909403)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-40, q=17; A=(3q-p)(p+q)^3=-1107197, B=-(p+3q)(p-q)^3=2037123. 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 19:57:14 UTC · history