Для авторизации:
curl 'http://jira.hillel.it:8080/rest/auth/1/session' -H "Content-Type: application/json" -X POST -d '{"username":"webinar5","password":"webinar5"}'


Для создания тикeта:
curl -X POST 'http://jira.hillel.it:8080/rest/api/3/issue' -b "JSESSIONID=AAA41251FCE2BDCE4ECEE70E9D4E3721;" -H 'Content-Type: application/json' --data '{"update":{"fields":{"project":{"id":"10324"},summary": "Api test issue by Artem","issuetype": {"id": "10000"},"assignee": {"name": "webinar5"}}}'