Let

- $E:y^2=x^3-x$ be an elliptic curve over $ \Bbb{Q}$ and
- $ω_E=dx/2y=dx/2\sqrt{x^3-x}$.

Then
$$
\begin{split}
\Omega(E)&=\int_{E(\Bbb{R})} ω_E\\
\\
&=2\int\limits_1^{+\infty} dx/\sqrt{x^3-x}
\end{split}
$$
**Question**. Let the Hasse-Weil $L$-function be $L(E,1)$.

How can I prove that
$$
L(E,1)/\Omega(E)=1/8\text{ ?} \label{1}\tag{$\star$}
$$
If you know any reference (★) is proved, I'll appreciate if you could show me how to calculate (★).