curve #2377

y² + xy = x³ − 111721208501x + 11359985343819105

a-invariants: [1, 0, 0, -111721208501, 11359985343819105]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 688677990
discriminant (Δ): 33496232448976788910481239779201600
Faltings height: 5.3386
naive height: 87.9314
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 71
regulator: 2.976281206030821251936190555480317443749
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:47 UTC
last updated: 2026-09-26 19:57:47 UTC

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

(-339402, 101072811)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-7, q=26; A=(3q-p)(p+q)^3=583015, B=-(p+3q)(p-q)^3=2551527. 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 19:57:47 UTC · history