Mordell-Weil groups of the Jacobian of the 5-th Fermat curve

Tzermias, Pavlos

doi:10.1090/S0002-9939-97-03637-X

Mordell-Weil groups of the Jacobian of the 5-th Fermat curve
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Proc. Amer. Math. Soc. 125 (1997), 663-668 Request permission

Abstract:

Let $J_{5}$ denote the Jacobian of the Fermat curve of exponent 5 and let $K=Q(\zeta _{5})$. We compute the groups $J_{5}(K)$, $J_{5}(K^{+})$, $J_{5}(Q)$, where $K^{+}$ is the unique quadratic subfield of $K$. As an application, we present a new proof that there are no $K$-rational points on the 5-th Fermat curve, except the so called “points at infinity".

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