curve #2305

y² + xy = x³ − 2222805152371x + 1274612535243160865

a-invariants: [1, 0, 0, -2222805152371, 1274612535243160865]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1047776730
discriminant (Δ): 1041373058455277920536895651754433600
Faltings height: 5.8378
naive height: 96.9030
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 37, 41
regulator: 3.660239142261719528824207343111142444313
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:53:19 UTC
last updated: 2026-09-26 19:53:19 UTC

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

(-1681006, 511728881)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=26; A=(3q-p)(p+q)^3=-153065, B=-(p+3q)(p-q)^3=10251927. 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 19:53:19 UTC · history