curve #2383

y² + xy + y = x³ − 91094146634x + 10190124875270396

a-invariants: [1, 0, 1, -91094146634, 10190124875270396]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 125832630
discriminant (Δ): 3520026082891749225711275176910400
Faltings height: 5.2016
naive height: 87.3191
primes of bad reduction: 2, 3, 5, 7, 11, 19, 47, 61
regulator: 5.857419335006074789283624225619176146290
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:08 UTC
last updated: 2026-09-26 19:58:08 UTC

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

(-207402, 142095688)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-40, q=7; A=(3q-p)(p+q)^3=-2192157, B=-(p+3q)(p-q)^3=-1972637. 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 19:58:09 UTC · history