Reducing a polynomial over a function field modulo a valuation

asked 2018-10-16 08:22:31 -0500

trbillin gravatar image

updated 2018-12-16 11:39:55 -0500

FrédéricC gravatar image

In my situation, I have the following elliptic curve:

K.<t> = FunctionField(QQ)
E = EllipticCurve([t,t])

I want to be able to go modulo t to get the curve

z*y^2 - x^3 = 0

I cannot figure out how to do this. I would like to work with valuations if possible (like going mod K.valuation(0)), but any way to make this work would be great. In general, I'd like to be able to go modulo any irreducible polynomial.

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