ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 09 Dec 2013 22:31:45 -0600Splitting field and mu invarianthttps://ask.sagemath.org/question/10556/splitting-field-and-mu-invariant/Please inform me how to compute the following two problems
1) Splitting field of a polynomial over Z, its degree of extension over Q and it's roots.
2) The mu invariant of other elliptic curves in an isogeny class from the mu invariant of the minimal curve in that isogeny class.
Sat, 21 Sep 2013 21:13:23 -0500https://ask.sagemath.org/question/10556/splitting-field-and-mu-invariant/Answer by John Cremona for <p>Please inform me how to compute the following two problems</p>
<p>1) Splitting field of a polynomial over Z, its degree of extension over Q and it's roots.</p>
<p>2) The mu invariant of other elliptic curves in an isogeny class from the mu invariant of the minimal curve in that isogeny class.</p>
https://ask.sagemath.org/question/10556/splitting-field-and-mu-invariant/?answer=15779#post-id-15779For question 1:
sage: R.<x> = ZZ[]
sage: f = x^3-2
sage: K.<a> = NumberField(f)
sage: L.<b> = K.galois_closure()
sage: L
Number Field in b with defining polynomial x^6 + 40*x^3 + 1372
Mon, 09 Dec 2013 22:31:45 -0600https://ask.sagemath.org/question/10556/splitting-field-and-mu-invariant/?answer=15779#post-id-15779