curve #2298

y² + xy + y = x³ − 1832357375503x + 952434674394533006

a-invariants: [1, 0, 1, -1832357375503, 952434674394533006]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 216868470
discriminant (Δ): 1859820330786202794712864649414062500
Faltings height: 5.8328
naive height: 96.3235
primes of bad reduction: 2, 3, 5, 7, 13, 19, 37, 113
regulator: 2.835679157129589672474269020099758655891
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:52:52 UTC
last updated: 2026-09-26 19:52:52 UTC

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

(733705, 54362822)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-38, q=25; A=(3q-p)(p+q)^3=-248261, B=-(p+3q)(p-q)^3=9251739. 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 19:52:52 UTC · history