ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 27 Sep 2016 07:16:07 -0500division_polynomial with integer coefficients?!http://ask.sagemath.org/question/23928/division_polynomial-with-integer-coefficients/Hi, I would like to get a Division-polynomial for an elliptic curve. The curve is
E=EllipticCurve(CC,[-35/4,-49/4])
I used the commands
E3 = E.change_ring(QQbar)
p = E3.division_polynomial(3, two_torsion_multiplicity=0)
and I obtained
3*x^4 - 105/2*x^2 - 147*x - 1225/16
Is there a way to get a division-polynomial which has integer coefficients and which is normalized?
Mon, 25 Aug 2014 10:55:29 -0500http://ask.sagemath.org/question/23928/division_polynomial-with-integer-coefficients/Comment by FrédéricC for <p>Hi, I would like to get a Division-polynomial for an elliptic curve. The curve is</p>
<pre><code>E=EllipticCurve(CC,[-35/4,-49/4])
</code></pre>
<p>I used the commands</p>
<pre><code>E3 = E.change_ring(QQbar)
p = E3.division_polynomial(3, two_torsion_multiplicity=0)
</code></pre>
<p>and I obtained</p>
<pre><code>3*x^4 - 105/2*x^2 - 147*x - 1225/16
</code></pre>
<p>Is there a way to get a division-polynomial which has integer coefficients and which is normalized? </p>
http://ask.sagemath.org/question/23928/division_polynomial-with-integer-coefficients/?comment=23930#post-id-23930What is the meaning of normalized ?Mon, 25 Aug 2014 11:55:23 -0500http://ask.sagemath.org/question/23928/division_polynomial-with-integer-coefficients/?comment=23930#post-id-23930Answer by John Cremona for <p>Hi, I would like to get a Division-polynomial for an elliptic curve. The curve is</p>
<pre><code>E=EllipticCurve(CC,[-35/4,-49/4])
</code></pre>
<p>I used the commands</p>
<pre><code>E3 = E.change_ring(QQbar)
p = E3.division_polynomial(3, two_torsion_multiplicity=0)
</code></pre>
<p>and I obtained</p>
<pre><code>3*x^4 - 105/2*x^2 - 147*x - 1225/16
</code></pre>
<p>Is there a way to get a division-polynomial which has integer coefficients and which is normalized? </p>
http://ask.sagemath.org/question/23928/division_polynomial-with-integer-coefficients/?answer=34972#post-id-34972The division polynomial does not depend on the base field so it would be more efficient to compute it from the original E rather than its base change to QQbar. You can always find the roots of the polynomial in QQbar later. It is also strange that you first defined the curve over CC since it has rational coefficients, but we do not know what you were planning to do.
Once you have a polynomial with coefficients in QQ you can scale it how you like, so this is not really a question about elliptic curves.Tue, 27 Sep 2016 07:16:07 -0500http://ask.sagemath.org/question/23928/division_polynomial-with-integer-coefficients/?answer=34972#post-id-34972