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Feb 4, 2011 at 18:32 comment added Franz Lemmermeyer D'accord - so I spelled it out for those of us who look at algebraic geometry as a mountain rather than a valley -)
Feb 4, 2011 at 9:23 comment added Pete L. Clark @Franz: since the (smooth projective model) of a hyperelliptic quartic is a genus one curve of index $1$ or $2$, this comes under the heading of my 1) above.
Feb 4, 2011 at 8:40 history answered Franz Lemmermeyer CC BY-SA 2.5