curve #2216

y² + xy + y = x³ − 40304114187459x + 98074666332214988746

a-invariants: [1, 0, 1, -40304114187459, 98074666332214988746]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 35977225830
discriminant (Δ): 34883125921226547215325262743016048668900
Faltings height: 6.6281
naive height: 105.5960
primes of bad reduction: 2, 3, 5, 7, 13, 23, 47, 73, 167
regulator: 5.795691493782018979051940123653576481732
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:47:40 UTC
last updated: 2026-09-26 19:47:40 UTC

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

(3897203, 437163918)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-26, q=47; A=(3q-p)(p+q)^3=1546587, B=-(p+3q)(p-q)^3=44736955. 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 19:47:40 UTC · history