curve #2233

y² + xy + y = x³ − x² − 17660065005923x + 10281739400963066531

a-invariants: [1, -1, 1, -17660065005923, 10281739400963066531]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 236306070
discriminant (Δ): 306829690613690760842970539322978885734400
Faltings height: 6.6532
naive height: 103.1206
primes of bad reduction: 2, 3, 5, 7, 11, 13, 43, 61
regulator: 8.841765665580971918187182414055529958741
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:48:43 UTC
last updated: 2026-09-26 19:48:43 UTC

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

(-4466105, 270709302)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-9, q=52; A=(3q-p)(p+q)^3=13118655, B=-(p+3q)(p-q)^3=33366207. 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 19:48:43 UTC · history