curve #2380

y² + xy + y = x³ − 158258669279x + 24193141004024606

a-invariants: [1, 0, 1, -158258669279, 24193141004024606]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 163162230
discriminant (Δ): 824460877517030001577053744812100
Faltings height: 5.2062
naive height: 88.9761
primes of bad reduction: 2, 3, 5, 7, 11, 23, 37, 83
regulator: 6.021538565973794035436831216584917257617
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:58 UTC
last updated: 2026-09-26 19:57:58 UTC

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

(804951/4, 177180881/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-14, q=23; A=(3q-p)(p+q)^3=60507, B=-(p+3q)(p-q)^3=2785915. 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 19:57:58 UTC · history