curve #2201

y² + xy = x³ − x² − 261483069817809x + 1627381369208908363113

a-invariants: [1, -1, 0, -261483069817809, 1627381369208908363113]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 8240622390
discriminant (Δ): 127267100854864074346084973559471605062500
Faltings height: 6.9448
naive height: 111.2058
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 41, 97
regulator: 7.237769990222095497952927125738705131378
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:46:44 UTC
last updated: 2026-09-26 19:46:44 UTC

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

(9393447, 40984104)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-42, q=55; A=(3q-p)(p+q)^3=454779, B=-(p+3q)(p-q)^3=112258779. 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 19:46:44 UTC · history