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Transactions of the American Mathematical Society

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The group of rational solutions of $ y\sp{2}=x(x-1)(x-t\sp{2}-c)$


Author: Charles F. Schwartz
Journal: Trans. Amer. Math. Soc. 259 (1980), 33-46
MSC: Primary 14H25; Secondary 10B05, 14H45, 14K20
MathSciNet review: 561821
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Abstract: In this paper, we show that the Mordell-Weil group of the Weierstrass equation $ {y^2}\, = \,x(x\, - \,1)(x\, - \,{t^2}\, - \,c),\,c \ne \,0,\,1$ (i.e., the group of solutions (x,y), with $ x,\,y\, \in \,{\textbf{C}}(t)$) is generated by its elements of order 2, together with one element of infinite order, which is exhibited.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0561821-X
Keywords: Weierstrass equation over function field, Mordell-Weil group, Gauss-Manin operator, modular forms, period relations
Article copyright: © Copyright 1980 American Mathematical Society