Modular compactifications of the space of pointed elliptic curves II
نویسندگان
چکیده
منابع مشابه
Modular Parametrizations of Elliptic Curves
Many — conjecturally all — elliptic curves E/Q have a "modular parametrization," i.e. for some N there is a map tp from the modular curve X0(N) to E such that the pull-back of a holomorphic differential on E is a modular form (newform) / of weight 2 and level N. We describe an algorithm for computing the degree of ip as a branched covering, discuss the relationship of this degree to the "congru...
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Suppose p is a prime of the form u + 64 for some integer u, which we take to be 3 mod 4. Then there are two Neumann–Setzer elliptic curves E0 and E1 of prime conductor p, and both have Mordell–Weil group Z/2Z. There is a surjective map X0(p) π −→ E0 that does not factor through any other elliptic curve (i.e., π is optimal), where X0(p) is the modular curve of level p. Our main result is that th...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2011
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x11005549