Generators of function fields of the modular curves 𝑋₁(5) and 𝑋₁(6)

Kim, Chang; Koo, Ja Kyung

doi:10.1090/S0025-5718-09-02303-5

Generators of function fields of the modular curves $X_1(5)$ and $X_1(6)$
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Abstract:

We show that the modular functions $j_{1,5}$ and $j_{1,6}$ generate function fields of the modular curves $X_1(N)$ ($N=5,6$, respectively) and find some number-theoretic properties of these modular functions.

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