Sudarshana chakra can not be termed as Astra. It was Sashtra.
Krishna did not need any mantra related to astra to invoke it.
In Mahabharat Agnidev brought it for Krishna during Khandav dahan.But we should not think that it was not with Krishna before. It always was with him but reached him through Agni in that avatar.
Pavaka then, addressing Krishna, said, 'With this, O slayer of Madhu, thou shalt be able without doubt to vanquish in battle even foes that are not human. With this weapon, without doubt, thou shalt be superior in battle to men and gods, and Rakshasas and Pisachas, and Daityas and Nagas. And thou shalt certainly be able with this to smite all. And, O Madhava, hurled by thee in battle at thy foes, this weapon will irresistibly slay the enemy and again come back into thy hands
The discus Sudarsana can be hurled without reciting any mantra. After killing the rival it then comes back into Krishna’s hands.
In Mahabharat we witnessed the death of Sishupala with this Sudarshana.
And while Sisupala was speaking thus, the exalted slayer of Madhu thought in his mind of the discus that humbleth the pride of the Asuras. And as soon as the discus came into his hands, skilled in speech the illustrious one loudly uttered these words,--'Listen ye lords of earth, why this one had hitherto been pardoned by me. As asked by his mother, a hundred offences (of his) were to be pardoned by me. Even this was the boon she had asked, and even this I granted her. That number, ye kings, hath become full. I shall now slay him in your presence, ye monarchs.' Having said this, the chief of the Yadus, that slayer of all foes, in anger, instantly cut off the head of the ruler of Chedi by means of his discus. And the mighty-armed one fell down like a cliff struck with thunder.
Sudarshan the discus ,the eternal weapon of Vishnu.
Yes. It belongs to Vishnu. It got great significance among the weapons of Vishnu that killed many asuras.
Yudhishtira happened to see the Sudarshana in embodied form,when he went to Vaikuntha.
It was not a mere weapon. It takes form whenever Vishnu desired..like in Ramavatar,
Vaishnava kshetras alott special place for Sudarshana in their worship formalities.
Chakrasnan ,bathing the Chakra in Pushkarini marks the end of Brahmotsav in Tirumala Tirupati,the highly acclaimed kshetras Of our age.
Vedanta Desikacharya hailed Sudarshana in his Ashtakam..recitation Of these verses cures illness and bestows good health.
The first verse of the ashtakam..
pratibhaṭaśreṇi bhīṣaṇa varaguṇastoma bhūṣaṇa
janibhayasthāna tāraṇa jagadavasthāna kāraṇa ।
nikhiladuṣkarma karśana nigamasaddharma darśana
jaya jaya śrī sudarśana jaya jaya śrī sudarśana ॥O shrI sudarshana! All the enemies of your Lord's devotees run away fearing
your prowess. All auspicious attributes find their home in you. Those ,
Who worship you cross the 'shoreless' ocean of Samsara and free themselves
from their cycles of births and deaths. The entire Universe is stabilized
by your mighty power. You cut asunder all the sins of those who approach
you as their refuge. You bless all of your devotees with the knowledge
about the righteous conduct prescribed by the Vedas. O Lord sudarshana
of these auspicious attributes! Hail to Thee! Hail to Thee!
Ignorant persons like Aswathama desired to hold the Sudarshana but failed to do so.
So Sudarshana was the eternal companion of Vishnu ,wielded by him in every yuga..
He doesn’t need any recitation Of mantra to hurl it.
Kisari Mohan Ganguli English Translation Adi Parva CCXXVII
Sabha Parva Section XLIV
Sudarshanashtakam by Vedanta deshikacharya translated by Sadagopan.