curve #2304

y² + xy = x³ − x² − 1218884484420x − 61594446665577600

a-invariants: [1, -1, 0, -1218884484420, -61594446665577600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 187435710
discriminant (Δ): 114256808794771615418008140898500272400
Faltings height: 5.9924
naive height: 95.1005
primes of bad reduction: 2, 3, 5, 7, 11, 17, 37, 43
regulator: 4.648713568598693447127732036376369334248
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:53:15 UTC
last updated: 2026-09-26 19:53:15 UTC

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

(-93408, 226859664)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-60, q=17; A=(3q-p)(p+q)^3=-8825277, B=-(p+3q)(p-q)^3=-4108797. 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 19:53:16 UTC · history