Elliptic Curves Over Number Fields with Prescribed Reduction Type

Name: Elliptic Curves Over Number Fields with Prescribed Reduction Type
Brand: Springer Fachmedien Wiesbaden
SKU: 9783528085698
Price: 223.65 PLN
Availability: InStock

Autor: Michael Laska

Język:

Oprawa: Miękka

Wydawca: Springer Fachmedien Wiesbaden

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Let K be an algebraic number field. The function attaching to each elliptic curve over K its conduct...

Informacje o książce

Autor

Michael Laska

Język

Niemiecki

Oprawa

Książka - Miękka

Data wydania

1983

strony

213

EAN

9783528085698

ISBN

352808569X

Enbook ID

02006371

Wydawca

Springer Fachmedien Wiesbaden

Waga

358

Wymiary

170 x 244 x 13

Pełny opis

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) .

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Elliptic Curves Over Number Fields with Prescribed Reduction Type

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