  We classify the automorphic Lie algebras of equivariant maps from a complex
torus to $\mathfrak{sl}_2(\mathbb{C})$. For each case we compute a basis in a
normal form. The automorphic Lie algebras correspond precisely to two disjoint
families of Lie algebras parametrised by the modular curve of
$\mathrm{PSL}_2(\mathbb{Z})$, apart from four cases, which are all isomorphic
to Onsager's algebra.
