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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Jacobian of the Klein curve


Author: Despina T. Prapavessi
Journal: Proc. Amer. Math. Soc. 122 (1994), 971-978
MSC: Primary 14H40; Secondary 14H45, 14H52
MathSciNet review: 1212286
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1212286-1
PII: S 0002-9939(1994)1212286-1
Article copyright: © Copyright 1994 American Mathematical Society