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how to generate Cayleygraph

asked 2019-06-17 06:10:26 -0500

manni gravatar image

Hello,

how can I generate a cayleygraph for

y^2 = x^3+ax ;

a, could be 1 or 2 or 3 ;

p = 17

The producer points should be identifiable in this graph.

Thanks

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answered 2019-06-17 23:52:54 -0500

Does this give what you want?

sage: E = EllipticCurve(GF(17), [1, 0]) # [1,0] -> coefficient of x, constant term
sage: E
Elliptic Curve defined by y^2 = x^3 + x over Finite Field of size 17
sage: A = E.abelian_group()
sage: G = A.permutation_group()
sage: G.cayley_graph()
Digraph on 16 vertices
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Thanks!! Can it be modified to see the points and subgroups? For example "Elliptic Curve defined by y^2 = x^3 + 6*x over Finite Field of size 7" Group "(4,2)" --> (1,0) --> (4,5) --> {} -->

manni gravatar imagemanni ( 2019-06-18 14:11:27 -0500 )edit

I don't know. You can look at the documentation for the cayley_graph method: http://doc.sagemath.org/html/en/refer...

John Palmieri gravatar imageJohn Palmieri ( 2019-06-18 15:18:20 -0500 )edit

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Asked: 2019-06-17 06:08:42 -0500

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Last updated: Jun 17