Abstract
Jacobi was the first person to suggest (in 1835) using the group law on a cubic curve E. The chord-tangent method does give rise to a group law if a point is fixed as the zero element. This can be done over any field over which there is a rational point.
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References
D.S. Nagaraj and B. Sury, A Quick Introduction to Algebraic Geometry and Elliptic Curves, this volume.
J. H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics 106, Springer-Verlag, New York 1986.
M. Tsfasman and S. Vladut, Algebraic geometric codes, Mathematics and its applications Vol. 58, Kluwer Academic Publishing Group 1991.
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© 2003 Hindustan Book Agency
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Sury, B. (2003). Elliptic Curves over Finite Fields. In: Bhandari, A.K., Nagaraj, D.S., Ramakrishnan, B., Venkataramana, T.N. (eds) Elliptic Curves, Modular Forms and Cryptography. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-15-6_3
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DOI: https://doi.org/10.1007/978-93-86279-15-6_3
Publisher Name: Hindustan Book Agency, Gurgaon
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