curve #2211

y² + xy = x³ − x² − 47244399591510x + 124184795533766446500

a-invariants: [1, -1, 0, -47244399591510, 124184795533766446500]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2399641290
discriminant (Δ): 86624918666168144925311117260290006080400
Faltings height: 6.6858
naive height: 106.0727
primes of bad reduction: 2, 3, 5, 17, 19, 23, 37, 97
regulator: 5.514558827646099244174266389350976877654
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:47:22 UTC
last updated: 2026-09-26 19:47:22 UTC

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

(-7929213, 520545009)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-60, q=37; A=(3q-p)(p+q)^3=-2080557, B=-(p+3q)(p-q)^3=46546323. 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 19:47:22 UTC · history