Paper Info
Title
Computing the degree of a modular parametrization
Abstract
The Weil-Taniyama conjecture states that every elliptic curve E/ of conductor N can be parametrized by modular functions for the congruence subgroup 0(N) of the modular group = PSL(2, ). Equivalently, there is a non-constant map from the modular curve X 0 (N) to E. We present here a method of computing the degree of such a map for arbitrary N. Our method, which works for all subgroups of finite index in and not just 0(N), is derived from a method of Zagier in [2]; by using those ideas, together with techniques which have been used by the author to compute large tables of modular elliptic curves (see [1]), we are able to derive an explicit and general formula which is simpler to implement than Zagier's. We discuss the results obtained, including several examples.
Year
DOI
Venue
1994
10.1007/3-540-58691-1_50
ANTS
Keywords
Field
DocType
modular parametrization,modular curve,modular function,elliptic curve,modular group,indexation
Modular form,Hecke operator,Discrete mathematics,Modular elliptic curve,Modular lambda function,Modular curve,Classical modular curve,Modular group,Elliptic curve,Mathematics
Conference
ISBN
Citations 
PageRank 
3-540-58691-1
0
0.34
References 
Authors
1
1
Name
Order
Citations
PageRank
John Cremona1144.46