curve #2524

y² + xy + y = x³ − 61803759x + 186858225646

a-invariants: [1, 0, 1, -61803759, 186858225646]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1217370
discriminant (Δ): 24072325913742594156900
Faltings height: 3.2179
naive height: 65.4320
primes of bad reduction: 2, 3, 5, 7, 11, 17, 31
regulator: 3.507360033396213132276202195660604041921
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:06:57 UTC
last updated: 2026-09-26 20:06:57 UTC

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

(-6187, 579648)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-10, q=7; A=(3q-p)(p+q)^3=-837, B=-(p+3q)(p-q)^3=54043. 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 20:06:58 UTC · history