ohhh man, sorry to burst your bubble but i don't think you have an authentic fender strat. it would've been great sana if you did.
first of all, fenders don't have 2 round string trees on one headstock. they only used one, and they only used it during the early 50's era. the tuners they used also on vintage strats are kluson tuners, yung round yung knobs and may butas yung tuning posts.
next, 1963-65 fenders used the pre-CBS logo, and it's not all black. or kung 1965 yan, they'd use the transition logo. i don't think meron na silang black fender logos during that time, i think they introduced them when the squiers and squier series fenders came out.
next, the two point trems were only introduced with the american standard strats and was later used on squier standard strats. so recent lang yan, in the 50's-60's era strats they used 6 screw trems and vintage "bent steel" saddles. that was the classic vintage trem design.
also, walang fender strat during that time that had the jack output at the bottom of the guitar. all had the football shaped jackplate. plus the serial number placement on vintage strats would be on the upper edge of the neckplate, not the center.
sorry bro, if you'd research pa sa ibang sites you'd find na walang strat like that.
http://www.stratcollector.com/http://www.provide.net/~cfh/fender.htmlnow, kung maganda tunog nung guitar na yan eh nako, walang issue kung orig or fake. actually it's not in the brand anyway, but in the tone, hehe. hope this is helpful bro! peace!