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Instantiating Elliptic Curve Isogenies using rational maps

asked 3 years ago

RKnebel gravatar image

updated 3 years ago

I have an elliptic curve E:y2=x3+x and the rational maps for a degree 14 isogeny ϕ=(ϕx,ϕy). I would like to get an Isogeny object using ϕx,ϕy so I can use some of the functionality of the Isogeny class, but I can't seem to find anything in the sagemath documentation about this.

Currently sage allows you to construct either cyclic isogenies by specifying a point P on E; or by the kernel polynomial provided the degree is either odd or the polynomial is divisible by x3+x.

EDIT: I've looked the the code of the EllipticCurveIsogeny class and the attributes for the x and y rational maps are private attributes. I cannot figure out a way to create an Isogeny object with my desired rational maps.

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answered 3 years ago

Luca gravatar image

This is not supported. Your best option is to pass the kernel polynomial, i.e., the denominator of ϕx, as lone paramter to E.isogeny(). This will not give you exactly the isogeny with ϕx,ϕy as rational maps, however you can compose that with an isomorphism to get the wanted isogeny.

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Asked: 3 years ago

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Last updated: Nov 03 '21