Also there's base 58 as used in all our BTC addresses

It's also a bastardisation of base 58 to avoid having 0, I, O and l
0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuv
becomes
123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz
base58 usually leaves out two of 0, O and o plus I and l.
Point of base58 is base 62 but w/o characters that are too similar.
I've not seen a lot of implementations but most I have seen keep 0 so that the first 10 are the same. bitcoin doesn't.
Also most I've seen have lower case letters before upper.
But there is no standard for base58 as far as I know.