  We provide an algorithm for computing an effective basis of homology of
elliptic surfaces over the complex projective line on which integration of
periods can be carried out. This allows the heuristic recovery of several
algebraic invariants of the surface, notably the N\'eron-Severi lattice, the
transcendental lattice, the Mordell-Weil group and the Mordell-Weil lattice.
This algorithm comes with a SageMath implementation.
