Can not use 'secp256k1' which is common on Crypto Currency to create JWT, Use 'secp256r1'

jwt-secp256k1-secp256r1.js

/* Common variables */
const JWT = require('jsonwebtoken');

// Payload
const payload = {
  sub: 'Subject',
  iss: 'Issuer',
  exp: 1639248876
}

let privateKey, token;


/******************************
 Wrong case using 'secp256k1'
*******************************/
const Elliptic = require('elliptic').ec;
const EC = new Elliptic('secp256k1');// Use 'secp256k1'

// Generate private key
privateKey = EC.genKeyPair().getPrivate().toString(16);

// Create token
token = JWT.sign(payload, privateKey, { algorithm: 'ES256'});

// Expected result is as follow.

/*
Error: error:0906D06C:PEM routines:PEM_read_bio:no start line
    at Sign.sign (crypto.js:331:26)
    at sign (/work/node_modules/jwa/index.js:76:45)
    at Object.sign (/work/node_modules/jwa/index.js:96:27)
    at Object.jwsSign [as sign] (/work/node_modules/jws/lib/sign-stream.js:32:24)
    at Object.module.exports [as sign] (/work/node_modules/jsonwebtoken/sign.js:188:21)
    at Object.<anonymous> (/work/jwt.js:24:13)
    at Module._compile (module.js:653:30)
    at Object.Module._extensions..js (module.js:664:10)
    at Module.load (module.js:566:32)
    at tryModuleLoad (module.js:506:12)
*/



/******************************
 Correct case using 'secp256r1'
*******************************/
const ECDSA = require('ecdsa-secp256r1');// Use 'secp256r1'

// Genarate private key
privateKey = ECDSA.generateKey();

// Retrive public key
const publicKey = privateKey.asPublic();

// Create token
token = JWT.sign(payload, privateKey.toPEM(), { algorithm: 'ES256'});

// Verify token
const decoded = JWT.verify(token, publicKey.toPEM());

console.log({ 
  privateKey: privateKey.toPEM(), 
  publicKey: publicKey.toPEM(), 
  token, 
  decoded 
});