curve #2215

y² + xy = x³ − 114720226555915x + 472893308330155490225

a-invariants: [1, 0, 0, -114720226555915, 472893308330155490225]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 8842689570
discriminant (Δ): 19991215637013478177608968373890625000000
Faltings height: 6.7579
naive height: 108.7342
primes of bad reduction: 2, 3, 5, 11, 13, 17, 29, 37, 113
regulator: 2.883858150038715402659276889461292551239
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:47:37 UTC
last updated: 2026-09-26 19:47:37 UTC

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

(6238250, 75134765)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=50; A=(3q-p)(p+q)^3=410839, B=-(p+3q)(p-q)^3=74410839. 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 19:47:37 UTC · history