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order finite field

asked 2020-05-17 02:22:26 -0500

Mati gravatar image

Hello

sage: E = EllipticCurve(GF(19),[0,3])
sage: E
Elliptic Curve defined by y^2 = x^3 + 3 over Finite Field of size 19e
sage: E.order()
13

How to calculate "13" ? i can understand, sorry i am new

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answered 2020-05-17 06:14:16 -0500

tmonteil gravatar image

updated 2020-05-17 12:37:43 -0500

slelievre gravatar image

You can get the source code of the order method by typing:

sage: E.order??

As you can see, this is basically a handler that decides which algorithm fits best since you did not specify one. In your case, it will use pari, so you have to look at the pari source code.

You can also have a look at

sage: E.cardinality_bsgs??

which implements "Mestre's trick", or

sage: E.cardinality_exhaustive??

which counts vertically over each x-value.

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Asked: 2020-05-17 02:22:26 -0500

Seen: 38 times

Last updated: May 17