curve #2502

y² + xy + y = x³ − 1115051099x + 14331249580466

a-invariants: [1, 0, 1, -1115051099, 14331249580466]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1009470
discriminant (Δ): 1386485606500090126222500
Faltings height: 3.7974
naive height: 74.1101
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23
regulator: 5.003094890605409025925515292147476054526
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:05:35 UTC
last updated: 2026-09-26 20:05:35 UTC

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

(-53685/4, 41529731/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=1; A=(3q-p)(p+q)^3=-231525, B=-(p+3q)(p-q)^3=-231173. 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 20:05:35 UTC · history