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In his page math.ucr.edu/home/baez/week229.html John Baez explains the way 4 points occur only once in the double cover of the 2-sphere by a 2-torus, every elliptic curve can be imagined to be. The fact that these 4 points can be chosen along the equator or as vertices touching the sphere of an ideal tetrahedron implies a relationship of the cross-ratio to the hyperbolic space with the sphere as boundary at infinity, something I still find mysterious.
I have read this in: en.wikipedia.org/wiki/Modular_lambda_function I can see it as cross ratio from the Legendre form of elliptic curve, but I do not see how it is that of the branch points of a ramified double cover of the projective line.
