Abstract
Many properties of (complex) elliptic curves are purely algebraic in the sense that they could also be derived in the field generated over the rationals by the two numbers g2 and g3, or perhaps in its algebraic closure. It is thus sufficient to work in a fixed field of characteristic zero (algebraically closed if needed). Our first aim will be to show that any non-singular (projective) plane cubic can be given in Weierstrass’ normal form. The study of the differentials over the curve (and their classification) will also be made purely in algebraic terms.
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(1973). Elliptic Curves in Characteristic zero. In: Elliptic Curves. Lecture Notes in Mathematics, vol 326. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46916-2_2
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DOI: https://doi.org/10.1007/978-3-540-46916-2_2
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