2010/02/28 by Andreas Schweizer · 8 citations
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Combinatorics #Cryptography and Residue Arithmetic #Degree (music) #Elliptic curve #Isogeny #Mathematical analysis #Mathematics #Physics #Statistics #Uniformization (probability theory) #math.AG #math.NT #msc:11G05 #msc:11G09 #msc:14J27
paper · pdf · doi:10.1016/j.jnt.2010.08.007
published in Journal of Number Theory 131(2), 285-299 (Elsevier BV) · published version, minor changes, new address, 20 pages, contains standard LaTeX-graphics
openalex publication_date 2010/10/17 · arxiv created 2010/10/22 · openalex created_date 2016/06/24 · arxiv updated 2016/10/06 · openalex updated_date 2026/08/05
We continue work of Gekeler and others on elliptic curves over \mathbb Fq(T) with conductor ∞⋅\mathfrak n where \mathfrak n∈\mathbb Fq[T] has degree 3. Because of the Frobenius isogeny there are infinitely many curves in each isogeny class, and we discuss in particular which of these curves is the strong Weil curve with respect to the uniformization by the Drinfeld modular curve X0(\mathfrak n). As a corollary we obtain that the strong Weil curve E/\mathbb Fq(T) always gives a rational elliptic surface over \mathbb Fq.