Solutions of equations from the paper
The Ising model: from elliptic curves to modular forms
and Calabi-Yau equations
(arxiv version here)
A. Bostan, S. Boukraa, S. Hassani, M. van Hoeij,
J.-M. Maillard, J-A. Weil and N. Zenine

Operators Z2, F2 and F3
Operators Z2, F2 and F3 can be found on the pages of Iwan Jensen : the page of Chi5, and the page for the L11 operator. A local (mirror) version can be found here.

Operators Ltilde3 and L4
The anihilating operator of Chi_6 factors as L46=L6*L23*L17.
L17 is operator (6) in the paper and factors (decomposes) as L17 = tildeL5 \oplus L3 \oplus (L4 * tildeL3 * L2)

The operator Ltilde3 and a solution in terms of 2F1 hypergeometric functions are here.
The other operators are in this file. Operator L4 has a 4F3 solutions (with a pullback)