A copy of the certification of rezoning together with the map and assessor’s parcel numbers for the rezoned land shall be recorded by the city or county in the recorder’s office in the same manner as deeds are recorded, and commencing on the lien date next following the effective date of the new zone, such land shall be assessed on the same basis as real property is assessed generally in that county. The assessor may require a description of the portion of the property rezoned as provided in Section 456 of the Revenue and Taxation Code.