Number Puzzle

Time for another puzzle. This is a somewhat simple one I found somewhere random on the internets:

There exists an natural number, N, for which all of the following statements are true:

1. N has 2 digits XOR N is even
2. N contains the digit "7” XOR N is prime
3. N is the product of two consecutive odd integers XOR N is one more than a perfect square
4. N is divisible by 11 XOR N is one more than a perfect cube
5. N is a perfect square XOR N has 3 digits

What is N?

For the statements where the puzzle refers to digits, it is meant to be digits in a base ten representation of course.

When I found this puzzle, I dismissed it as being stupid and probably not worth the effort. I'm glad I gave it another shot though, the answer is somewhat pleasing to find. I'll admit its not amazing, but it shouldn't take more than 10 minutes and it is nice to work through the details.