No. If there was, you could calculate the entire private key and bitcoin (and elliptic curve multiplication) would be entirely broken.

Take public key K which corresponds to private key k. With G being the generator point, then k*G = K.

If you can work out whether k is odd or even knowing only K, then you can work out whether the last bit of k is 1 or 0. You can then take the multiplicative inverse of 2 of K, which has the effect of halving your private key, which shifts all the bits one position to the right (you would have to do K+(-G) first if the last bit was 1, so you are halving an even number). You can then work out whether the new k is odd or even knowing your new K. You can then repeat this process for the entire length of the private key until you know the full key and then spend the coins.