Thanks to Dami Lee for patiently walking through how to compute the period matrix of this 12-fold cyclic cover of a thrice punctured sphere, and thanks Matthias Weber for showing me how to write the 3 fold cover of a 5-punctured sphere as a 12-fold cyclic cover of a thrice punctured sphere. Most of the figures are either hand-drawn or made using Geogebra. Note that I will sometimes use $\tau$ to denote $2 \pi$. All errors are mine and mine alone.

*Motivational Sidenote:*

* This is part of my project in attempting to understand the notion of height in terms of the symmetry of the underlying variety in formal group law theory. *

*Though it may seem disparate, this post is the computation of the Jacobian of a Shiga curve shown to have height 3 properties by Sebastien Thyssen and Hanno van Woerden. I suspect that the Jacobian of this curve is indeed my abelian variety constructed as a variety with complex multiplication in my last post under the guidance of Kato. * Continue reading Calculating the Period Matrix of a Shiga Curve, $y^3 = x^4-1$.