curve #2277

y² + xy + y = x³ − 29328099696463x + 61132331956828951406

a-invariants: [1, 0, 1, -29328099696463, 61132331956828951406]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2045228010
discriminant (Δ): 22448954150587084272520639297851562500
Faltings height: 6.3387
naive height: 104.6423
primes of bad reduction: 2, 3, 5, 7, 17, 41, 89, 157
regulator: 4.825882292316730680727865521432321982074
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:31 UTC
last updated: 2026-09-26 19:51:31 UTC

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

(3134925, 13114162)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=41; A=(3q-p)(p+q)^3=53851, B=-(p+3q)(p-q)^3=37546875. 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 19:51:31 UTC · history