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2013-01-13 02:26:34 +0100 asked a question Extension degree over function field

Hello!

I would like to compute the extension degree over a function field.

So I use the commend "degree()". But I found it didn't work well. It produces always just the degree of the polynomial.

For example,

sage: K.<x> = FunctionField(QQ)
sage: R.<y> = K[]
sage: L.<y> = K.extension(y^2 - (x^2)); L
Function field in y defined by y^2 - x^2
sage: L.degree()
2

In fact, the extension degree [L:K] = 1.

What's wrong?

I'd appreciate it if you could let me know how to compute the extension degree over a function field?

Thank you!

2012-08-18 10:06:59 +0100 asked a question Abelian varieties attached to modular forms

Hello!

I have two questions:

  1. How to compute the Mordell-Weil rank of an abelian variety attached to a moduar form?

  2. How to factor a Q-simple abelian variety attached to a modular form into elliptic curves over a number field.

Thank you!