  We give a criterion to distinguish between a genus three Jacobian and its
[-1] twist in terms of the product of the 36 even theta nulls.
  We also express the product of the 36 theta nulls in terms of the
discriminant of a genus three curve.
  The results are arithmetic in nature and thus add to previous work over C on
the product of the even theta nulls. They generalize previous work of
Ritzenthaler and Lachaud for Abelian threefolds which are (2,2,2) isogenous to
a product of elliptic curves.
  This answers a 2003 of letter of Jean-Pierre Serre to Jaap Top.
