No, you can't have 13 fish unless they are very tiny. The trouble with saying 13 fish is that doesn't take into account how big the fish are. Using Thinkfish's calculator, you can have 25cm fish. That means you add up the adult length of fish you want and if it comes to more than 25cm, the tank is overstocked. To fit 13 fish in there, they would all have to be 2cm long when fully grown.
But there's more to stocking than just the size of the fish. You also need to take behaviour into account. Some fish need to be in a group of the same fish; some are fast swimmers so although they would fit they wouldn't have enough swimming room; some fish like some bettas (siamese fighting fish) won't tolerate any other fish so that would be the only fish you could have in there.
Small tanks should be stocked less heavily than big ones. With fewer fish, the water stays more stable, and when the water in a small tank becomes unstable, it happens very quickly and can kill your fish before you notice.
Here is a list of the only fish you can have in that tank. Just one from the list, in the number that the list gives.
Siamese fighting fish (Betta) 1.
Endler's livebearer (Poecilia wingei) 8.
Boraras Brigattae (Mosquito Rasbora or Chili Rasbora). 6
Danio Margaritatus (Celestial Pearl Danio). 6
Hyphessobrycon Amandae (Ember Tetra). 6
Microdevario Kubotai (Green Neon Rasbora). 6
Aplocheilichthys Normani (Norman's Lampeye). 6
Microrasbora Erithromicron (Emerald Dwarf Rasbora). 6
Microrasbora gatesi. 6
Microrasbora kubotai. 6
Microrasbora nana. 6
Microrasbora rubescens. 6
Boraras maculatus (Dwarf rasbora, Dwarf-spotted rasbora, Spotted rasbora, Pygmy rasbora). 6
Boraras merah. 6
Boraras micros. 6
Boraras urophthalmoides (Least rasbora, Exclamation-point rasbora). 6
Mosquito Fish/Gambusia
Aphyosemion striatum (Red-Striped Killifish). 1m 2f
Epiplatys Annulatus (Clown Killifish). 1m 2f
Nothobranchius Rachovii (Bluefin Nothobranch). 1m 2f
List pinched from another siteSo
one shoal of six OR a trio of the killifish at the end of the list.
Not all these fish are suitable for beginners, you should read up on them first. Take note of what pH and hardness these fish need, and find out what your tapwater is like. You will need a test kit whichever way you cycle the tank, and that will have a pH tester. Your water supplier's website should tell you somewhere what your hardness is. Choose fish that suit your tap water.
Fishless cycling is easier as you don't have to do daily water changes to keep the fish alive.
fishless cylingcycling with fish