Canto 1 - Boyhood
Bāla-kāṇḍa
Chapter 45: The Churning of the Milk Ocean
Text 1.45.40-41

तुरगं देवराजाय कौस्तुभं केशवाय च।
धन्वन्तरिर्महातेजा लोकरक्षणतत्परः॥

आयुर्वेदमयो राम तथा साधारणः स्मृतः।
सुरासुराश्च गन्धर्वाः क्षोभयामासुरम्बुधिम्॥

turagaṁ deva-rājāya kaustubhaṁ keśavāya ca
dhanvantarir
mahā-tejā loka-rakṣaṇa-tat-paraḥ

āyurvedamayo rāma tathā sādhāraṇaḥ smṛtaḥ
surāsurāś
ca gandharvāḥ kṣobhayām āsur ambudhim

turagam = the horse was considered to belong to; deva-rājāya = the king of the devas; kaustubham = Kaustubha; keśavāya ca = was considered to belong to Lord Keśava; dhanvantariḥ = and Dhanvantari; mahā-tejāḥ = of great prowess; loka-rakṣaṇa-tat-paraḥ = focused on protecting the world; āyurvedamayaḥ = and filled with knowledge of Āyurveda; rāma = O Rāma; tathā sādhāraṇaḥ smṛtaḥ = was considered to be common to all; sura-asurāḥ ca = the suras, asuras; gandharvāḥ = and gandharvas; kṣobhayām āsuḥ = churned; ambudhim = the ocean [further].

O Rāma, the horse was considered to belong to the king of the devas, Kaustubha was considered to belong to Lord Keśava, and Dhanvantari of great prowess, focused on protecting the world and filled with knowledge of Āyurveda, was considered to be common to all. The suras, asuras and gandharvas churned the ocean [further].

In Bhagavad-gītā 10.27, Lord Kṛṣṇa, the Supreme Lord, mentions Uccaiḥśravā and Airāvata:

uccaiḥśravasam aśvānāṁ
viddhi
mām amṛtodbhavam
airāvataṁ
gajendrāṇāṁ

“Of horses know Me to be Uccaiḥśravā, produced during the churning of the ocean for nectar. Of lordly elephants I am
Airāvata.”

Śrīla Prabhupāda explains why the Lord mentions these two celestial animals as His representatives in his purport to this Bhagavad-gītā verse: “The devotee demigods and the demons (asuras) once took part in churning the sea. From this churning, nectar and poison were produced, and Lord Śiva drank the poison. From the nectar were produced many entities, of which there was a horse named Uccaiḥśravā. Another animal produced from the nectar was an elephant named Airāvata. Because these two animals were produced from nectar, they have special significance, and they are representatives of Kṛṣṇa.”