curve #2364

y² + xy + y = x³ − 187332642234x − 4374159879791204

a-invariants: [1, 0, 1, -187332642234, -4374159879791204]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 45513930
discriminant (Δ): 412480827434488514609847944059347600
Faltings height: 5.5239
naive height: 89.4821
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 61
regulator: 3.308021038403806796700698017624353655651
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:59 UTC
last updated: 2026-09-26 19:56:59 UTC

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

(-419326, 21362448)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-44, q=17; A=(3q-p)(p+q)^3=-1869885, B=-(p+3q)(p-q)^3=1588867. 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 19:56:59 UTC · history