τῇ ὑπὸ Ἡροδότου γεγραμμένῃ βίβλῳ
τῆς ὑπὸ Φαρνελλος γεγραμμένης βίβλου, κτλ
With the perfect passive (including participles), you should always use the dative of agent, not υπο + genitive.
1488. Dative of the Agent.—With passive verbs (usually in the perfect and pluperfect) and regularly with verbal adjectives in -τός and -τέος, the person in whose interest an action is done, is put in the dative. The notion of agency does not belong to the dative, but it is a natural inference that the person interested is the agent.
ἐμοὶ καὶ τούτοις πέπρα_κται has been done by (for) me and these men D. 19.205, ““ἐπειδὴ αὐτοῖς παρεσκεύαστο” when they had got their preparations ready” T. 1.46, ““τοσαῦτά μοι εἰρήσθω” let so much have been said by me” L. 24.4, ““ἐψηφίσθαι τῇ βουλῇ” let it have been decreed by the senate” C.I.A. /lref>
a. With verbal adjectives in -τός and -τέος (2149): ““τοῖς οἴκοι ζηλωτός” envied by those at home” X. A. 1.7.4, ““ἡμῖν γ᾽ ὑπὲρ τῆς ἐλευθερία_ς ἀγωνιστέον” we at least must struggle to defend our freedom” D. 9.70. For the accus. with -τέον, see 2152 a.
1490. The dative of the agent is rarely employed with other tenses than perfect and pluperfect: ““λέγεται ἡμῖν” is said by us” P. L. 715b, τοῖς Κερκυ_ραίοις οὐχ ἑωρῶντο the ships were not seen by (were invisible to) the Corcyraeans T. 1.51; present, T. 4.64, 109; aorist T. 2.7.