from a smooth curve of genus 2, we may identify the Jacobian with under the map . We now observe two facts: Since is a hyperelliptic curve the map from the symmetric product to , defined by , is the blow down of the graph of the hyperelliptic involution to the canonical divisor class. Moreover, the canonical map is a double cover. Hence we get a double cover .

This double cover is the one which already appeared above: The 6 lines are the images