curve #2316

y² + xy + y = x³ − 744043169108x + 208053877092626306

a-invariants: [1, 0, 1, -744043169108, 208053877092626306]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1404172770
discriminant (Δ): 7662015648259349573408668167962250000
Faltings height: 5.7984
naive height: 93.6197
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 107
regulator: 2.739035759991168734734129189109324039213
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:53:56 UTC
last updated: 2026-09-26 19:53:56 UTC

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

(313701, 74123719)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-44, q=21; A=(3q-p)(p+q)^3=-1301869, B=-(p+3q)(p-q)^3=5217875. 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 19:53:56 UTC · history