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ON j-INVARIANTS OF WEIERSTRASS EQUATIONS
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 Title & Authors
ON j-INVARIANTS OF WEIERSTRASS EQUATIONS
Horiuchi, Ryutaro;
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 Abstract
A simple proof of the fact that the j-invariants for Weierstrass equations are invariant under birational transformations which keep the forms of Weierstrass equations is given by finding a non-trivial explicit birational transformation which sends a normalized Weierstrass equation to the same equation.
 Keywords
j-invariant;Weierstrass equation;elliptic curve;coverings;Riemann surface of genus one;
 Language
English
 Cited by
 References
1.
H. Cohen, A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics, 138, Springer-Verlag, Berlin, 1993

2.
J. Harris, Algebraic Geometry, Graduate Texts in Mathematics, 133, Springer-Verlag, New York, 1993

3.
R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, Springer-Verlag, New York, 1977

4.
J. H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, 106. Springer-Verlag, New York, 1986