curve #2423

y² + xy + y = x³ − 30769804069x − 560440779808324

a-invariants: [1, 0, 1, -30769804069, -560440779808324]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3116190
discriminant (Δ): 1728777395862191739822830035632900
Faltings height: 5.0689
naive height: 84.0630
primes of bad reduction: 2, 3, 5, 7, 11, 19, 71
regulator: 6.201746798144566430730409961884490791647
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:40 UTC
last updated: 2026-09-26 20:00:40 UTC

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

(197673, 32782858)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-38, q=11; A=(3q-p)(p+q)^3=-1397493, B=-(p+3q)(p-q)^3=-588245. 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 20:00:40 UTC · history