# How to find the generator of an elliptic curve? [duplicate]

If the elliptic curve has prime order of points, then all of its points are generator. Is this true? If so, how can I find the optimized generator(which generates more number of points) among them?

• Yes, I think so @Gilles – Venkatesh Feb 6 '17 at 10:36
• If you agree that your question is a duplicate, please click the button “That solves my problem” to confirm. – Gilles 'SO- stop being evil' Feb 6 '17 at 11:02

• @Venkatesh if cofactor $\neq1$ it means the curve has not prime order. Its order will in fact be cofactor times the prime order of the generator which NIST shows. – Ruggero Feb 6 '17 at 9:54