curve #2271

y² + xy = x³ − x² − 4718795443119x + 3899460082075915833

a-invariants: [1, -1, 0, -4718795443119, 3899460082075915833]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 927728010
discriminant (Δ): 155811107667525120164279615190800062500
Faltings height: 6.1353
naive height: 99.1613
primes of bad reduction: 2, 3, 5, 11, 19, 31, 37, 43
regulator: 4.196152740833146732885126222363222907740
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:06 UTC
last updated: 2026-09-26 19:51:06 UTC

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

(-2467568, 721407029)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-18, q=37; A=(3q-p)(p+q)^3=884811, B=-(p+3q)(p-q)^3=15472875. 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 19:51:06 UTC · history