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Lattices in the sense of discrete subgroups of Euclidean spaces, as used in number theory, discrete geometry, Lie groups, etc. (Not to be confused with lattice theory or lattices as used in physics! For lattices (ordered sets), use the tag: [lattice-theory])
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Neron-Severi Lattice of Elliptic K3
Usually, the really hard part of this problem is to find a basis for the Mordell-Weil group, not to calculate the N\'eron-Severi group. You suggest that somehow you are capable to find a basis for the …