curve #2197

y² + xy = x³ − 96194765616180x + 299114643271374176400

a-invariants: [1, 0, 0, -96194765616180, 299114643271374176400]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 54222955710
discriminant (Δ): 18317579736546233203018619961792765504000000
Faltings height: 7.0195
naive height: 108.2058
primes of bad reduction: 2, 3, 5, 7, 11, 17, 43, 163, 197
regulator: 6.117764522430964575970438057626647712435
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:46:29 UTC
last updated: 2026-09-26 19:46:29 UTC

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

(7584600, 2410483980)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=60; A=(3q-p)(p+q)^3=15662879, B=-(p+3q)(p-q)^3=74414879. 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 19:46:29 UTC · history