curve #2278

y² + xy + y = x³ − 3412297341743x + 1335147290757357806

a-invariants: [1, 0, 1, -3412297341743, 1335147290757357806]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1795934910
discriminant (Δ): 1772757605941160919797732262618164062500
Faltings height: 6.2290
naive height: 98.1888
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 29, 83
regulator: 5.112579199833635809491981385033606014358
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:35 UTC
last updated: 2026-09-26 19:51:35 UTC

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

(-1982115, 559041682)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-58, q=25; A=(3q-p)(p+q)^3=-4779621, B=-(p+3q)(p-q)^3=9720379. 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 19:51:35 UTC · history