curve #2610

y² + xy = x³ − 85482602918516x + 304203846939171027600

a-invariants: [1, 0, 0, -85482602918516, 304203846939171027600]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 4294920630
discriminant (Δ): 1536142732043788823072994061259673600
Faltings height: 6.4688
naive height: 107.8516
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 47, 179
regulator: 13.1520845709902824796775899713527779758570
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:35 UTC
last updated: 2026-09-26 20:12:35 UTC

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

(5291344, 183755620)
(5334268, 12051976)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=44; A=(3q-p)(p+q)^3=-4833, B=-(p+3q)(p-q)^3=64053535. 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 20:12:35 UTC · history