Read Elliptic Curves over Number Fields with Prescribed Reduction Type

Elliptic Curves over Number Fields with Prescribed Reduction Type

Michael Laska

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Description:Let K be an algebraic number field. The function attaching to each elliptic curve over K its conductor is constant on isoger. y classes of elliptic curves over K (for the definitions see chapter 1). ~Ioreover, for a given ideal a in OK the number of isogeny classes of elliptic curves over K with conductor a is finite. In these notes we deal with the following problem: How can one explicitly construct a set of representatives for the isogeny classes of elliptic curves over K with conductor a for a given ideal a in OK? The conductor of an elliptic curve over K is a numerical invariant which measures, in some sense, the badness of the reduction of the elliptic curve modulo the prime ideals in OK' It plays an important role in the famous Weil-Langlands conjecture on the connection between elliptic curves over K and congruence subgroups in 5L2(OK) * In case K ~ this connection can be stated as follows. For any ideal a = (N) in ~ let ro(N) be the congruence subgroup ro(N) { (: ~) E 5L2 (~) c E (N) } of 5L2 (~) and let 52 (fo (N» be the space of cusp forms of weight 2 for r 0 (N) Now Weil conjectured that there exists a bijection between the rational normalized eigenforms in 52(ro(N» for the Heckealgebra and the - 2 - Lsug~ny classes uf elliptic curves over ~ with conductor a = (N) .We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Elliptic Curves over Number Fields with Prescribed Reduction Type. To get started finding Elliptic Curves over Number Fields with Prescribed Reduction Type, you are right to find our website which has a comprehensive collection of manuals listed.
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Pages: 228

Format: PDF, EPUB & Kindle Edition

Publisher: Vieweg+teubner Verlag

Release: 1983

ISBN: yfjUAAAAMAAJ

Description: Let K be an algebraic number field. The function attaching to each elliptic curve over K its conductor is constant on isoger. y classes of elliptic curves over K (for the definitions see chapter 1). ~Ioreover, for a given ideal a in OK the number of isogeny classes of elliptic curves over K with conductor a is finite. In these notes we deal with the following problem: How can one explicitly construct a set of representatives for the isogeny classes of elliptic curves over K with conductor a for a given ideal a in OK? The conductor of an elliptic curve over K is a numerical invariant which measures, in some sense, the badness of the reduction of the elliptic curve modulo the prime ideals in OK' It plays an important role in the famous Weil-Langlands conjecture on the connection between elliptic curves over K and congruence subgroups in 5L2(OK) * In case K ~ this connection can be stated as follows. For any ideal a = (N) in ~ let ro(N) be the congruence subgroup ro(N) { (: ~) E 5L2 (~) c E (N) } of 5L2 (~) and let 52 (fo (N» be the space of cusp forms of weight 2 for r 0 (N) Now Weil conjectured that there exists a bijection between the rational normalized eigenforms in 52(ro(N» for the Heckealgebra and the - 2 - Lsug~ny classes uf elliptic curves over ~ with conductor a = (N) .We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Elliptic Curves over Number Fields with Prescribed Reduction Type. To get started finding Elliptic Curves over Number Fields with Prescribed Reduction Type, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Elliptic Curves over Number Fields with Prescribed Reduction Type

Elliptic Curves over Number Fields with Prescribed Reduction Type

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