Help with HA API query

Attempting to query the HA API according to the docs. I wish to pass both an end_time and filter on filter_entity_id. However the following results in an error:

now_encoded = urllib.parse.quote_plus(datetime.now().isoformat())
query = '{}api/history/period/{}?end_time={}?filter_entity_id={}'.format(url, lookback_period, now_encoded, entity)
response = get(query, headers=headers).json()

Out[59]:
{'message': 'Invalid end_time'}

However if I remove the filter_entity_id then I don’t get any errors, but data is returned for all of my entities (slow!). Therefore there must be a problem with the way I am stringing end_time and filter_entity_id together. Any ideas?