how to generate Cayleygraph

asked 2019-06-17 13:10:26 +0200

manni
1 ●1

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

answered 2019-06-18 06:52:54 +0200

John Palmieri

8551 ●19 ●71 ●186 http://www.math.washin...

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 ( 2019-06-18 21:11:27 +0200 )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 ( 2019-06-18 22:18:20 +0200 )edit

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