curve #2347

y² + xy + y = x³ − 3663108133273x + 2698489707696661256

a-invariants: [1, 0, 1, -3663108133273, 2698489707696661256]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 60357990
discriminant (Δ): 27626866180436170623424233578062500
Faltings height: 5.8064
naive height: 98.4016
primes of bad reduction: 2, 3, 5, 7, 11, 17, 29, 53
regulator: 5.315927427484035573239473147686440857608
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:55:55 UTC
last updated: 2026-09-26 19:55:55 UTC

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

(-2109930, 1018107802)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=29; A=(3q-p)(p+q)^3=-15125, B=-(p+3q)(p-q)^3=13252491. 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 19:55:55 UTC · history