Elliptic curve of order $p = 2q + 1$

Does anyone know an example of an Elliptic Curve of caracteristic $$p$$ ($$E_p$$) that has a point generator $$G$$ that generates a subgroup of order $$q$$, with $$p$$, $$q$$ being prime numbers and $$p = 2q + 1$$?

• Possible duplicate elliptic curves of prime order – kelalaka Feb 7 at 16:57
• I suspect that any such curve would be supersingular, and so (unless you're doing isogenies) wouldn't be a good idea for crypto – poncho Feb 7 at 17:09
• @fgrieu: I believe he's talking about the characteristic – poncho Feb 7 at 17:10
• @fgrieu: With $p$ I mean the modulus of the field of the Elliptic Curve. Is that the characteristic? – Fiono Feb 7 at 17:13
• A finite elliptic curve is based on some finite field $GF(p^k)$. The characteristic of the curve is actually defined to be $p$; however since you have $k=1$, that's the same. fgrieu was confused because 'order' is more typically used to mean 'the size of the (sub)group' (which is how you used it the second time) – poncho Feb 7 at 17:17