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division_polynomial with integer coefficients?!

asked 2014-08-25 10:55:29 -0600

pittersen gravatar image

updated 2015-01-13 14:02:18 -0600

FrédéricC gravatar image

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?

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What is the meaning of normalized ?

FrédéricC gravatar imageFrédéricC ( 2014-08-25 11:55:23 -0600 )edit

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answered 2016-09-27 07:16:07 -0600

John Cremona gravatar image

The 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.

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Asked: 2014-08-25 10:55:29 -0600

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Last updated: Sep 27 '16