how to generate Cayleygraph

asked 5 years ago

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 5 years ago

John Palmieri

8916 ●20 ●74 ●193 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

link

Comments

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 ( 5 years ago )

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

John Palmieri ( 5 years ago )

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