# Elliptic Curve functions don't seem to exist?

Hello. I'm trying to design a puzzle that involves finding a weakness in an elliptic curve cryptography application. I see descriptions of past puzzles that others have made, but they use SAGE with commands like "E = EllipticCurve(GF(c), [a, b])". From my attempts to uses SAGE online before installing, and from looking through the manual, it looks like there aren't any functions called EllipticCurve or for that matter GF. (They show up with red underlines in the online command window.) But then I did try running a similar command anyway: "sage: p = 354990952970600489 sage: E = EllipticCurve(GF(p),[9326,1376127157])" and got an error about this being prime or something similar -- don't have the error in front of me. So do the functions exist or what? I'm puzzled because the tutorial doesn't seem to work despite being written specifically for SAGE.

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Is it possible that you ran it all as one command? @achrzesz has the right way to think about it. If you are in the notebook (not command line) interface, you can remove the "sage: " part from these.

( 2013-02-05 08:35:26 -0600 )edit

(The red underlinneess3209 are probably from your browser's spell-check; at least, that's what I geeeeet when I misspeelell things, and it wouldn't know about GF or EllipticCurve.)

( 2013-02-05 08:36:37 -0600 )edit

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sage: p=354990952970600489
sage: E = EllipticCurve(GF(p),[9326,1376127157])
sage: E
Elliptic Curve defined by y^2 = x^3 + 9326*x + 1376127157 over Finite Field of size 354990952970600489

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