what is the public information in Elliptic curve cryptosystems
To generate your pair of keys with elliptic curves first you have to chose your domain parameters (I think this name may comes from the P1363 naming convention, or perhaps it's previous).

Those domain parameters will be public. For example for curves over finite fields those parameters are: ${p,a,b,G,n,h}$. The lower level operations will be made in $\mathbb{F}_p$ and the operations will be made using points on a curve. Then $a$ and $b$ (or the equivalents is uses different notation) is also public and also the equation used. About the generator point $\langle G\rangle$, you can think like public it is in DLP over finite fields.

About the order of the cyclic subgroup of points where the ECDLP is defined is public ($ord(G)=n$), together with the cofactor $h$ (that shall be very small number and both primes, with relation $h \lll n$), and the product of them is the number of points of the curve.

The only thing secret is the secret key, often labelled as $d$, where the public key is $P=d[G]$.