curve #2274

y² + xy = x³ − 6246101661416x + 6002836800076468800

a-invariants: [1, 0, 0, -6246101661416, 6002836800076468800]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1178595210
discriminant (Δ): 29068545601056521412347806566531993600
Faltings height: 6.1044
naive height: 100.0025
primes of bad reduction: 2, 3, 5, 13, 17, 23, 59, 131
regulator: 4.221985909813714515351882887052182217843
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:17 UTC
last updated: 2026-09-26 19:51:17 UTC

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

(1525438, 155542846)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=36; A=(3q-p)(p+q)^3=287807, B=-(p+3q)(p-q)^3=17457215. 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 19:51:17 UTC · history