Geodesic
Modular Parametrizations of Elliptic Curves
Canadian mathematical bulletin, Tome 28 (1985) no. 3, pp. 372-384

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DOI

Many — conjecturally all — elliptic curves E/ have a "modular parametrization," i.e. for some N there is a map φ from the modular curve X 0(N) to E such that the pull-back of a holomorphic differential on E is a modular form (newform) f of weight 2 and level N. We describe an algorithm for computing the degree of φ as a branched covering, discuss the relationship of this degree to the "congruence primes" for f (the primes modulo which there are congruences between f and other newforms), and give estimates for the size of this degree as a function of N.
DOI : 10.4153/CMB-1985-044-8
Mots-clés : 14K07, 10D12, 10D23 
Zagier, D. Modular Parametrizations of Elliptic Curves. Canadian mathematical bulletin, Tome 28 (1985) no. 3, pp. 372-384. doi: 10.4153/CMB-1985-044-8
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     author = {Zagier, D.},
     title = {Modular {Parametrizations} of {Elliptic} {Curves}},
     journal = {Canadian mathematical bulletin},
     pages = {372--384},
     year = {1985},
     volume = {28},
     number = {3},
     doi = {10.4153/CMB-1985-044-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-044-8/}
}
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