Abstract
Its is known that the Jacobian J of the Klein curve is isogenous to E 3 {{\mathbf {E}}^3} for a certain elliptic curve E. We compute explicit equations for E and prove that J is in fact isomorphic to E 3 {{\mathbf {E}}^3} . We also identify the subgroup of J generated by the image of the Weierstrass points of the curve under an Albanese embedding, and we show that it is isomorphic to Z / 2 Z × ( Z / 7 Z ) 3 {\mathbf {Z}}/2{\mathbf {Z}} \times {({\mathbf {Z}}/7{\mathbf {Z}})^3} .
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