His great @-@ grandfather was Consul in 36 BC ( in replacement , and abdicated ) , and Governor of Asia in the same year . His grandfather became Consul Suffect in July of either 21 or 22 , and was known as a personal friend of Emperor Tiberius ( AD 14 – 37 ) , accompanying the emperor during his voluntary seclusion on Capri from 23 onwards , dying in 33 . Nerva 's father , finally , attained the consulship in 40 under emperor Caligula ( 37 – 41 ) . The Cocceii were connected with the Julio @-@ Claudian dynasty through the marriage of Sergia Plautilla 's brother Octavius Laenas , and Rubellia Bassa , the great @-@ granddaughter of Tiberius .