[pilaf]

> only two irregular verbs

This is what textbooks often say, but it's kind of a soft lie. Besides the typical する and 来る (which are strongly irregular), there's:

ある → ない (negative form)

行く → 行って instead of expected 行いて

くれる → くれ (imperative form) instead of expected くれろ

And a number of others.

https://en.wikipedia.org/wiki/Japanese_irregular_verbs

[glandium]

I'll go pedantic, but ない is technically not an irregular negative form of ある. The negative form of ある is the regular あらぬ/あらない, but it has been substituted with ない, which is an entirely different word. You'll often hear あらへん in Kansai dialect, which is derived from ある.

Edit: there are idioms that use あらず which is also a standard negative form of ある, like なきにしもあらず.