Written in this form, carbon-13, what does the 13 represent and what is the atomic number?

Explanation:
Carbon has 3 isotopes. Carbon-12, Carbon-13, and Carbon-14
All of them have an atomic number of 6, which means all of them have 6 protons (if they had different numbers of protons, they'd be different elements).
Since they all have 6 protons, in their elemental forms, they all have 6 electrons, too.
Carbon-12:
Atomic number: 6
Mass number: 12
protons: 6
electrons: 6
neutrons: 6
Carbon-13:
Atomic number: 6
Mass number: 13
protons: 6
electrons: 6
neutrons: 7
Carbon-14:
Atomic number: 6
Mass number: 14
protons: 6
electrons: 6
neutrons: 8