curve #2345

y² + xy + y = x³ − 1542153151169x + 737074892619452576

a-invariants: [1, 0, 1, -1542153151169, 737074892619452576]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1613722110
discriminant (Δ): 29917297138910932028435482124900100
Faltings height: 5.6656
naive height: 95.8062
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 29, 109
regulator: 3.100500369375604184590499855730574972403
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:55:47 UTC
last updated: 2026-09-26 19:55:47 UTC

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

(-323913/4, 7425361529/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=29; A=(3q-p)(p+q)^3=37387, B=-(p+3q)(p-q)^3=8622315. 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 19:55:47 UTC · history