I would also include the name of the church, location, identification of the specific register.
Larger towns, and certainly the cities, can have several churches, more than religious denomination. The larger the parish, the more registers they will have, and some of these registers can have overlapping dates.
Some registers will have folio numbers rather than page numbers. A folio is numbered only the front, and the reference include whether the cited record is on the front (“recto”) or back (“verso”).