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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 fit best since you did not provide one. In your case, it will use pari, so you have to look at the pari source code.

You can have a look at

sage: E.cardinality_bsgs??

which implements "Mestre's trick", or

sage: E.cardinality_exhaustive??

which counrs vertically over each x-value.

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 fit best since you did not provide 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 counrs vertically over each x-value.

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 fit fits best since you did not provide 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 counrs counts vertically over each x-value.