Encrypt with elliptic curves
While it is possible to encrypt using elliptic curves, typically some form of hybrid encryption is used (for performance reasons or because the algorithm supports only a few bytes of data). Typically an Integrated Encryption Schemes is used.

In these systems, another symmetric (AEAD) algorithm (AES in some modern and strong mode, Chacha+Poly1305, or a symmetric cipher and a MAC) is used to do the encryption, and the asymmetric algorithm is used to do a key agreement (typical in case of ECC) or key exchange (typical in case of RSA).

The key agreement process typically employed is based on Diffie-Hellman key exchange.



If you want an off-the-shelve program to encrypt data using ECC as key agreement, have a look at GPG. Versions beyond 2.1 have support for a handful of curves.

If you want to write a program that uses ECC, you will have to find a library that does ECC DH, or better yet, have a library that does the combination of key exchange and symmetric encryption for you (the so called seal and open operations), like NaCl or libsodium.