curve #2461

y² + xy + y = x³ − 4916152293x + 61508931234556

a-invariants: [1, 0, 1, -4916152293, 61508931234556]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 65555490
discriminant (Δ): 5969814121021410990935667562500
Faltings height: 4.6004
naive height: 78.5610
primes of bad reduction: 2, 3, 5, 7, 11, 13, 37, 59
regulator: 4.236630259095057060719095832350215352213
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:03:00 UTC
last updated: 2026-09-26 20:03:00 UTC

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

(-36265, 13878132)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-26, q=11; A=(3q-p)(p+q)^3=-199125, B=-(p+3q)(p-q)^3=354571. 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 20:03:01 UTC · history