curve #2230

y² + xy + y = x³ − x² − 18249065964617x + 29605930425724894409

a-invariants: [1, -1, 1, -18249065964617, 29605930425724894409]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1303332030
discriminant (Δ): 10304587789741682692142987983980096000000
Faltings height: 6.4794
naive height: 103.2190
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 37
regulator: 2.594862753661161587403352240896216628528
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:48:32 UTC
last updated: 2026-09-26 19:48:32 UTC

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

(-4892433, 1337906716)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-21, q=44; A=(3q-p)(p+q)^3=1861551, B=-(p+3q)(p-q)^3=30483375. 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 19:48:33 UTC · history