generate ES512 and RS256 elliptic curve keypairs for JWT JWK (JSON Web Token JSON Web Key) using openssl

index.sh

# RS256
# private key
openssl genrsa -out rs256-4096-private.rsa 4096
# public key
openssl rsa -in rs256-4096-private.rsa -pubout > rs256-4096-public.pem

# ES512
# private key
openssl ecparam -genkey -name secp521r1 -noout -out ecdsa-p521-private.pem
# public key
openssl ec -in ecdsa-p521-private.pem -pubout -out ecdsa-p521-public.pem 

test.js

// from npmjs.org/jwa. shout out to brianloveswords
const fs = require('fs');
const jwa = require('jwa');
const privateKey = fs.readFileSync(__dirname + '/ecdsa-p521-private.pem');
const publicKey = fs.readFileSync(__dirname + '/ecdsa-p521-public.pem');

const ecdsa = jwa('ES512');
const input = 'very important stuff';

const signature = ecdsa.sign(input, privateKey);
console.log('signature', signature)
console.log('verify', ecdsa.verify(input, signature, publicKey))

Verify and read parameters:
openssl ec -in ecdsa-p521-private.pem -text