I was asked to calculate all the possible groups for elliptic curves and their order in $\mathbb{F}_5$. There are $p^2-p$ groups that respect $\Delta \neq 0$, so there are $20$ groups.
Some of them may be isomorphic. I have to look for the ones with the same order.
For example: are the ones defined by $x^3+4x+2$ and $x^3+4x+3$ isomorphic? The points of the first groups are $(3,1), (3,4), (\infty, \infty)$, for the second group are $(2,2), (2,3), (\infty, \infty)$
How do I check if they are isomorphic or not?
If I understand you correctly you have two groups of order three which means they are isomorphic as there only is one group of order $3$ up to isomorphism.