
Elliptic Curves over Number Fields with Prescribed Reduction Type
Michael Laska(Author)
Vieweg+Teubner Verlag
Published on 1. January 1983
Book
Paperback/Softback
213 pages
978-3-528-08569-8 (ISBN)
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) .
More details
Series
Edition
1983
Language
German
Place of publication
Wiesbaden
Germany
Publishing group
Vieweg & Teubner
Target group
Professional and scholarly
Research
Illustrations
213 S.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 13 mm
Weight
389 gr
ISBN-13
978-3-528-08569-8 (9783528085698)
DOI
10.1007/978-3-322-87599-0
Schweitzer Classification
Other editions
Additional editions

E-Book
03/2013
Vieweg+Teubner Verlag
€42.99
Available for download
Content
1. Reduction of elliptic curves.- 2. Elliptic curves with good reduction outside a given set of prime ideals.- 3. The diophantine equation x3 ? y2 = r.- 4. Isogeny Classes.- 5. Review on explicit results.- References.- Index of special symbols.