curve #2391

y² + xy + y = x³ − 204027929794x + 35461336950675476

a-invariants: [1, 0, 1, -204027929794, 35461336950675476]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 56573790
discriminant (Δ): 318399556614775800703661351174400
Faltings height: 5.2086
naive height: 89.7382
primes of bad reduction: 2, 3, 5, 7, 13, 17, 23, 53
regulator: 6.477932368128815046793569163062852437271
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:38 UTC
last updated: 2026-09-26 19:58:38 UTC

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

(-111845/4, 1622837491/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-16, q=23; A=(3q-p)(p+q)^3=29155, B=-(p+3q)(p-q)^3=3143907. 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 19:58:39 UTC · history