Thanks for your interest in our product ZAPI.
You can obtain the corresponding test cycle id by opening the below url (in the format as mentioned below) in your browser
You can also pass either of the below query parameters to filter down and check for corresponding test cycle id
Also I am not sure if you are aware of our documentation link for Zephyr for JIRA APIs already buts till pasting the link below for your reference.
Hope the above mentioned helps you in answering your queries.
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