curve #2410

y² + xy = x³ − 63240262966x + 6111455302100900

a-invariants: [1, 0, 0, -63240262966, 6111455302100900]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3504270
discriminant (Δ): 51620517383572599735220738560000
Faltings height: 4.9761
naive height: 86.2242
primes of bad reduction: 2, 3, 5, 7, 11, 37, 41
regulator: 4.496968112615591984487958208471785299366
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:59:53 UTC
last updated: 2026-09-26 19:59:53 UTC

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

(-896125/4, 761322715/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=4; A=(3q-p)(p+q)^3=-1760913, B=-(p+3q)(p-q)^3=-1723025. 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 19:59:53 UTC · history