ECDSA x,y coordinate validity verification doesn't seem to work
The plain text format of this equation only makes sense when you understand the theory behind it.  y ^ 2 = x ^ 3 + 7 mod P means "do all math in this equation using the finite number field with definition P".  It might better be written (y^2 = x^3 +7) mod p.

To keep the math simple, lets simply subtract one side from the other to see if that evaluates to zero.  This lets us avoid roots. Here's code using the Python interactive shell, e.g. python from a command prompt):

&gt;&gt;&gt; x = 55066263022277343669578718895168534326250603453777594175500187360389116729240
&gt;&gt;&gt; y = 32670510020758816978083085130507043184471273380659243275938904335757337482424
&gt;&gt;&gt; p = 115792089237316195423570985008687907853269984665640564039457584007908834671663
&gt;&gt;&gt; (x**3 + 7 - y**2) % p
0