curve #2217

y² + xy = x³ − 47755534973581x + 126894462534718811345

a-invariants: [1, 0, 0, -47755534973581, 126894462534718811345]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2534390430
discriminant (Δ): 14141504328586429962859627450137444993600
Faltings height: 6.6160
naive height: 106.1050
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 31, 59
regulator: 5.611157348389398489196669899942878883701
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:47:44 UTC
last updated: 2026-09-26 19:47:44 UTC

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

(4161728, 477466121)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-55, q=38; A=(3q-p)(p+q)^3=-830297, B=-(p+3q)(p-q)^3=47457063. 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 19:47:44 UTC · history