curve #2374

y² + xy = x³ − 127126426466x − 7838128798611900

a-invariants: [1, 0, 0, -127126426466, -7838128798611900]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 6926010
discriminant (Δ): 104948021408669982472902847915622400
Faltings height: 5.4146
naive height: 88.3189
primes of bad reduction: 2, 3, 5, 7, 13, 43, 59
regulator: 6.795868571067229308251298225621706514902
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:36 UTC
last updated: 2026-09-26 19:57:36 UTC

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

(-97500, 60296910)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-43, q=16; A=(3q-p)(p+q)^3=-1791153, B=-(p+3q)(p-q)^3=1026895. 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 19:57:36 UTC · history