# What is Mordell-Weil lattice?

What is Mordell-Weil lattice?

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It is Mordell-Weil group equipped with Néron-Tate pairing (see Silverman's book for the definition of these objects). –  François Brunault Jun 25 '10 at 11:26
I have voted to close: FB's comment is the correct answer. No need for others to get involved. –  Pete L. Clark Jun 25 '10 at 20:12
Almost correct: it's the quotient of the MW group by the torsion group, equipped with the Néron-Tate pairing. –  Noam D. Elkies Apr 27 '12 at 18:53
Hm, even that's not quite right for a constant curve with non-torsion points... So form the quotient by the subgroup of points of height zero (which contains the torsion group). –  Noam D. Elkies Apr 28 '12 at 2:54