On the Jacobian of the Klein curve

Prapavessi, Despina T.

doi:10.1090/S0002-9939-1994-1212286-1

On the Jacobian of the Klein curve
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by Despina T. Prapavessi

Proc. Amer. Math. Soc. 122 (1994), 971-978

DOI: https://doi.org/10.1090/S0002-9939-1994-1212286-1

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Abstract:

Its is known that the Jacobian J of the Klein curve is isogenous to ${{\mathbf {E}}^3}$ for a certain elliptic curve E. We compute explicit equations for E and prove that J is in fact isomorphic to ${{\mathbf {E}}^3}$. 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 ${\mathbf {Z}}/2{\mathbf {Z}} \times {({\mathbf {Z}}/7{\mathbf {Z}})^3}$.

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