curve #2308

y² + xy = x³ − 3494722017910x + 2514195389121640100

a-invariants: [1, 0, 0, -3494722017910, 2514195389121640100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 52222170
discriminant (Δ): 855171638472169761324370012224000000
Faltings height: 5.8982
naive height: 98.2604
primes of bad reduction: 2, 3, 5, 7, 11, 13, 37, 47
regulator: 2.143064573197369507352307898342501564823
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:53:30 UTC
last updated: 2026-09-26 19:53:30 UTC

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

(1065620, 13976090)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=28; A=(3q-p)(p+q)^3=-88209, B=-(p+3q)(p-q)^3=12907375. 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 19:53:30 UTC · history