Universal elliptic functions

For the elliptic curve defined by the most general form $y^2 + (\mu_1 x + \mu_3) y = x^3 + \mu_2 x^2 + \mu_4 x + \mu_6$, we show the power series expansion of Weierstsass sigma function $\sigma (u)$ at the origin is of Hurwitz integral over $\mathbb{Z}[{\mu }_1\mathrm{/}2,{\mu }_2,{\mu }_3,{\mu }_4,{\mu }_6]$. Namely, the coefficient $c_n$ of any term $c_n{u}^n\mathrm{/}n!$ of the expansion belongs to $\mathbb{Z}[{\mu }_1\mathrm{/}2,{\mu }_2,{\mu }_3,{\mu }_4,{\mu }_6]$. The last section contains several first terms of $n$-plication equation of the curve.