Editing Kummer surface (section)

=== Weil pairing ===
The 2-torsion points on an Abelian variety admit a symplectic [[bilinear form]] called the Weil pairing. In the case of Jacobians of curves of genus two, every nontrivial 2-torsion point is uniquely expressed as a difference between two of the six Weierstrass points of the curve. The Weil pairing is given in this case by
<math>\langle p_1-p_2,p_3-p_4\rangle=\#\{p_1,p_2\}\cap\{p_3,p_4\}</math>. One can recover a lot of the group theoretic invariants of the group <math>Sp_4(2)</math> via the geometry of the <math>16_6</math> configuration.