curve #2279

y² + xy + y = x³ − 3089733551909x + 1980904429954442396

a-invariants: [1, 0, 1, -3089733551909, 1980904429954442396]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 294692790
discriminant (Δ): 192583015639666503466650820308590062500
Faltings height: 6.0993
naive height: 97.8909
primes of bad reduction: 2, 3, 5, 7, 17, 23, 37, 97
regulator: 4.911673276909442691169209606832471802322
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:39 UTC
last updated: 2026-09-26 19:51:39 UTC

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

(1283751, 360050932)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-14, q=37; A=(3q-p)(p+q)^3=1520875, B=-(p+3q)(p-q)^3=12867147. 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 19:51:39 UTC · history