curve #2647

y² + xy = x³ − 31856980791x + 2118076661752425

a-invariants: [1, 0, 0, -31856980791, 2118076661752425]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 224970690
discriminant (Δ): 131094448441250617176575832129600
Faltings height: 4.9322
naive height: 84.1672
primes of bad reduction: 2, 3, 5, 7, 17, 29, 41, 53
regulator: 37.8113412339573433901087400747980526977544
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:15:16 UTC
last updated: 2026-09-26 20:15:16 UTC

Witness: 2 independent points log in to add more points →

(-158862, 56379741)
(-337009/4, 519045625/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-35, q=6; A=(3q-p)(p+q)^3=-1292617, B=-(p+3q)(p-q)^3=-1171657. 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 20:15:16 UTC · history