Universal elliptic functions

For the elliptic curve defined by the most general form $y^2 + (μ_1 x + μ_3) y = x^3 + μ_2 x^2 + μ_4 x + μ_6$, we show the power series expansion of Weierstsass sigma function $σ(u)$ at the origin is of Hurwitz integral over $\mathbb{Z}[μ_1/2, μ_2, μ_3, μ_4, μ_6]$. Namely, the coefficient $c_n$ of any term $c_n u^n/n!$ of the expansion belongs to $\mathbb{Z}[μ_1/2, μ_2, μ_3, μ_4, μ_6]$. The last section contains several first terms of $n$-plication equation of the curve.

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