curve #2294

y² + xy = x³ − 2121074472166x + 1186484663051881700

a-invariants: [1, 0, 0, -2121074472166, 1186484663051881700]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 223092870
discriminant (Δ): 2581459841354944250740513188505190400
Faltings height: 5.8651
naive height: 96.7624
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23
regulator: 3.338974512695796624969556865144302581067
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:52:37 UTC
last updated: 2026-09-26 19:52:37 UTC

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

(-1678612, 131442506)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-19, q=32; A=(3q-p)(p+q)^3=252655, B=-(p+3q)(p-q)^3=10214127. 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 19:52:37 UTC · history