curve #2433

y² + xy + y = x³ − 20932616359x + 1030848455041046

a-invariants: [1, 0, 1, -20932616359, 1030848455041046]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 20930910
discriminant (Δ): 127951058506179012099940921076100
Faltings height: 4.8901
naive height: 82.9073
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 41
regulator: 3.004506501791261549697673799299979351382
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:01:18 UTC
last updated: 2026-09-26 20:01:18 UTC

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

(-156191, 22213208)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=7; A=(3q-p)(p+q)^3=-1082565, B=-(p+3q)(p-q)^3=-895973. 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 20:01:18 UTC · history