I'm not sure what you mean. We need first person plural definite conjugation (because we have a definite object here), which is -juk/jük. Now, the j assimilates after certain consonants in writing (& therefore in speech too), such as s, sz, z, zs, c, cs, dz & dzs if there's even a word ending with dzs.
I'm not quite sure what you mean, ismer is completely regular.
The sentence has ismerjük, first person plural definite (we know it.)
Ismeri is third person singular definite (it knows it), ismerje is third person singular definite but with imperative mood (it should know it.)
For third person singular in present tense with indicative mood, indefinite conjugation has no ending (ismer, it knows something), definite conjugation has -ja or -i (ismeri, it knows it.) But here we have first person plural. You're talking about "him/her/it", while the sentence is about "us."
Okay, I think I get what the problem is.
In Hungarian most suffixes have two or three forms. The form you should use depends on the so-called vowel harmony (Turkish has a similar system, you seem to be familiar with that language.) The so-called back (or deep) vowels are a, á, o, ó, u, ú. The so-called front (or high) vowels are e, é, i, í, ö, ő, ü, ű. In case of some suffixes there are two front vowel forms, an unrounded (e, é, i, í) & a rounded (ö, ő, ü, ű), but that isn't interesting in our case.
For 3rd person singular in present tense with indicative mood & definite conjugation there are two forms, -ja & -i. Here are some examples:
kap - kapja
mar - marja
lát - látja
tud - tudja
olvas - olvassa (here's the assimilation thing I talked about because I thought you were confused about that)
ismer - ismeri
üt - üti
süt - süti
The forms of most suffices differ usually only in the vowels, so this particular one might seem strange & can be confusing, I think.