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Is computing dual isogenies broken?

asked 2017-09-26 09:11:43 -0500

janwil gravatar image

Hi all,

I am trying to find duals of elliptic curve isogenies. I am following the example in the official documentation in the "Elliptic curves" section:

sage: k = GF(11)
sage: E = EllipticCurve(k,[1,1])
sage: Q = E(6,5)
sage: phi = E.isogeny(Q)
sage: phi.dual()

and I get the error

NotImplementedError: currently no algorithms for computing the Weierstrass p-function for that characteristic / precision pair is implemented. Lower the precision below char(k) - 2

Is there something I am doing wrong or is there indeed a bug? The problem manifests itself both wihs Sage7 and Sage8, on Linux and macOS and on SageCell.

Best, Jan

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answered 2017-09-26 18:07:40 -0500

For elliptic curves over finite fields, it seems computing dual isogenies currently only works if the field's characteristic is at least four times the degree plus seven.

Improving isogenies in Sage is the object of several trac tickets. See

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Asked: 2017-09-26 09:11:43 -0500

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Last updated: Sep 26