Yes, you are surely eligible for JEE Advanced. 

Since ST cut off is 44.3345172 as declared by NTA. 

And since you have got more than this, you are surely eligible. 

JEE Advanced application form is available from May 3 to May 9.

Good Luck for your preparation. 

Hello aspirant,

You have secured 51 percentile with ST category, minimum qualified marks for st category is 27. And minimum percentile is around 44.3. So yes you will be appeared for jee advance. 

For more detail you may check out the link:

https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/articles/jee-main-cutoff/amp&ved=2ahUKEwit84f2x_zhAhXkQ3wKHY4FDmkQFjAMegQIAxAC&usg=AOvVaw0ay0p7xaI0Sc82xeEH0ED5&ampcf=1&cshid=1556790382233

Best of luck!!