Code
At the present moment there are a few repositories available, but I am planning to upload some Magma code in the next few months, supporting the theoretical results in:
(with Aleksander Horawa) Balanced triple product p-adic L-functions and Stark points (ArXiv).
Approximations of the balanced triple product p-adic L-function (ArXiv), Journal of Number Theory, Volume 246 (May 2023), pp. 189-226.
Some geodesics
Hereafter you can have a look at some interesting drawings that I recently made with the Software SageMath.
Some of them appear in Special curves in modular surfaces by M. Tamiozzo.
The code considered here is trivial as it amounts to calling the function list_plot on the real and imaginary part of the j-invariant, e.g. for Z_10:
p=list_plot( [(elliptic_j(sqrt(10)*cos(t/10000)+sqrt(10)*I*sin(t/10000)).real(),
elliptic_j(sqrt(10)*cos(t/10000)+sqrt(10)*I*sin(t/10000)).imag())
for t in range(1, 31415, 1) ],
plotjoined=False, color='blue', size=1, aspect_ratio=1 )