curve #2411

y² + xy = x³ − 54166580756x + 4834436730898320

a-invariants: [1, 0, 0, -54166580756, 4834436730898320]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2065170
discriminant (Δ): 74620731575003111557913640960000
Faltings height: 4.9699
naive height: 85.7596
primes of bad reduction: 2, 3, 5, 23, 41, 73
regulator: 4.972334684705876533606500957307248154305
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:59:57 UTC
last updated: 2026-09-26 19:59:57 UTC

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

(-264032, 27145516)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-25, q=16; A=(3q-p)(p+q)^3=-53217, B=-(p+3q)(p-q)^3=1585183. 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 19:59:57 UTC · history