Conductor of an elliptic curve in GP/Pari

Question

I'm looking for a function that takes in as its input an elliptic curve and gives as an output the conductor of the curve. This should be a really simple built-in function to Pari, but frustratingly the code

E = ellinit("11a1");
E.conductor

Gives the error "* at top-level: E.conductor ^--------- not a function in function call * Break loop: type 'break' to go back to GP prompt"

Even though once E is defined typing E. and then using tab twice lists E.conductor as a built in function for elliptic curve objects. I've looked all over Pari's elliptic curve reference card and elliptic curves function list with no luck.

Any help would be really appreciated!

Answer 1

I don't know anything about elliptic curves, so this might not be helpful. I had a quick look through the help.

If you have the name of the elliptic curve as in "11a1", then you can get the conductor with ellconvertname("11a1") which returns [11, 0, 1]. The conductor is just the first element: 11.

Otherwise there is a method ellglobalred that given an elliptic curve structure will return amongst other things the arithmetic conductor. (I'm not sure if that is the same thing, but in this case the first element contains 11).

And I also noticed that after calling ellglobalred, the information including conductor gets stored back into the elliptic curve structure. You can then extract this using indexes. For example E=ellinit("11a1"); ellglobalred(E); E[16][6][1]