AIR-2A Genie on F-104 true or false ?

I was watching this programme called "flying through time" which this
week was about the century series fighters from f-100 to f-106 and it
mentioned that the f-104 toted the genie rocket as one of its weapon
options .
Now this programme usually gives info whilst givin the wrong imagery
or both but it did show a zipper with a weird retractable centerline
pylon supposedly for a big honking genie as so the programme is leadin
the viewer to believe .
Is this a genuine capability for a Starfighter? I would have thought
it wouldn't have the loading capacity for such a weapon or even the
software to launch it unlike the F-102 or F-106