curve #2606

y² + xy + y = x³ − 9331040659629x + 10968175240962417556

a-invariants: [1, 0, 1, -9331040659629, 10968175240962417556]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2587775190
discriminant (Δ): 26051661930985841756525651441018208900
Faltings height: 6.1591
naive height: 101.2067
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 37, 137
regulator: 12.9905190824388035612515268591605101374321
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:19 UTC
last updated: 2026-09-26 20:12:19 UTC

Witness: 2 independent points log in to add more points →

(1705181, 122106882)
(1733768, 43164603)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-26, q=37; A=(3q-p)(p+q)^3=182347, B=-(p+3q)(p-q)^3=21253995. 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 20:12:20 UTC · history