curve #2261

y² + xy + y = x³ − x² − 16569333686498x + 25955846290618245281

a-invariants: [1, -1, 1, -16569333686498, 25955846290618245281]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 176832810
discriminant (Δ): 94580492106237131235108666834974030400
Faltings height: 6.2885
naive height: 102.9293
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 79
regulator: 3.293811469303829409405037075088233004076
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:28 UTC
last updated: 2026-09-26 19:50:28 UTC

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

(2296005, 126440227)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-45, q=34; A=(3q-p)(p+q)^3=-195657, B=-(p+3q)(p-q)^3=28103223. 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 19:50:28 UTC · history