curve #2341

y² + xy + y = x³ − 2582910858433x + 1597735040292873056

a-invariants: [1, 0, 1, -2582910858433, 1597735040292873056]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 273788130
discriminant (Δ): 37694711863242919197029499552562500
Faltings height: 5.7560
naive height: 97.3534
primes of bad reduction: 2, 3, 5, 7, 11, 29, 61, 67
regulator: 4.801642409577602787961730668268817503139
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:55:32 UTC
last updated: 2026-09-26 19:55:32 UTC

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

(-1849895, 213769502)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-58, q=3; A=(3q-p)(p+q)^3=-11147125, B=-(p+3q)(p-q)^3=-11122069. 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 19:55:32 UTC · history