curve #2382

y² + xy + y = x³ − 97538206344x − 4906954438273274

a-invariants: [1, 0, 1, -97538206344, -4906954438273274]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 209725230
discriminant (Δ): 48987012804886419552506763233859600
Faltings height: 5.3503
naive height: 87.5241
primes of bad reduction: 2, 3, 5, 11, 13, 19, 31, 83
regulator: 3.945643688695388551900685826835751883903
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:05 UTC
last updated: 2026-09-26 19:58:05 UTC

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

(-140894, 77779487)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-44, q=13; A=(3q-p)(p+q)^3=-2472653, B=-(p+3q)(p-q)^3=-925965. 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 19:58:05 UTC · history