Modular Functions

  • Dale Husemöller
Part of the Graduate Texts in Mathematics book series (GTM, volume 111)


Every elliptic curve E over the complex numbers C corresponds to a complex torus C/L τ with L τ = Z τ + Z and τ ∈ ℌ, the upper half plane, where C/L τ is isomorphic to the complex torus of complex points E(C) on E. In the first section we show easily that C/L τ and C/L τ′ are isomorphic if and only if there exists
$$\left( {\begin{array}{*{20}{c}} a & b \\ c & d \\ \end{array} } \right) \in S{L_2}\left( z \right)$$
$$ \tau ' = \frac{{a\tau + b}}{{c\tau + d}}.$$


Riemann Surface Modular Form Elliptic Curve Half Plane Elliptic Curf 
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Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Dale Husemöller
    • 1
  1. 1.Department of MathematicsHaverford CollegeHaverfordUSA

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