Modular transformations of elliptic Feynman integrals

We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through suitable transformation we can achieve that nome squared is small quantity, leading to fast numerical evaluations. Contrary case multiple polylogarithms, where it sufficient consider just variable transformations for evaluations more natural in combination (i.e. transformation) together with redefinition master integrals. Thus combine coordinate on base manifold basis fibre. Only two stay within same class functions.