Richard in Reading on Wed, 12 Jun 2013 16:55:16 +0200

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How to calculate lower degree factors of elldivpol(e,100)

 To: pariusers@pari.math.ubordeaux1.fr
 Subject: How to calculate lower degree factors of elldivpol(e,100)
 From: Richard in Reading <richard_in_reading@yahoo.co.uk>
 Date: Wed, 12 Jun 2013 15:55:01 +0100 (BST)
 Deliverydate: Wed, 12 Jun 2013 16:55:16 +0200
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I'm interested in the lower degree factors of various divison polynomials.
I'm very impressed with PARI's ability to calculate with and then factorize a polynomials with large coefficients and degrees in the thousands. I have used the following:
e=ellinit("1584s1");
f=elldivpol(e,100);
fordiv(100,d,if(d!=100,f=f/gcd(f,elldivpol(e,d))));
ff=factor(f);
apply(poldegree,ff[,1]~)
%1 = [100, 100, 200, 200, 1000, 2000]
But this is slow. Is there a more direct way to calculate the factors of degree 100 without getting the larger factors?
I'm calculating these polynomials in order to evaluate them at certain integer values. Is there perhaps a way of calculating these values directly. For instance:
x=1;factor(eval(ff[1,1])
%2 = [2, 290; 3, 220]
Any theoretical guidance on finding factors of small degree for larger torsion would also be very welcome!
Thanks!
Richard