The canonical height is
(1)
It is a quadratic form, vanishes on torsion points, and satisfies for every isogeny .
The regulator is the determinant of the canonical-height pairing on a basis of the free part of the Mordell-Weil group. A unimodular basis change leaves it invariant.

Ancestors (10)

  1. Naive height on the projective line
  2. Elliptic curve
  3. Genus one curve
  4. Geometric genus
  5. Normalization of an algebraic curve
  6. Algebraic geometry
  7. Geometry and topology
  8. Area of mathematics
  9. Mathematics
  10. Home

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