The comments above give already the answer, but for the sake of completeness let us be a bit more precise.

Let $E/\mathbb{Q}$ be an elliptic curve. Let $\Omega^{+}$ be the smallest positive element in the period lattice $\Lambda$. Then the conjecture of Birch and Swinnerton-Dyer predicts that

$$
\frac{L^{*}(E,1)}{[E(\mathbb{R}):E(\mathbb{R})^{o}] \cdot \Omega^{+}} = \frac{\prod_{p} c_p \cdot | Sha| \cdot Reg}{| E(\mathbb{Q})_{tors}|^2}
$$

The denominator on the left, where the index is the number of connected components of $E(\mathbb{R})$, can also be written as the *absolute value* of $\int_{E(\mathbb{R})}\omega_E$ where $\omega_E$ is a invariant differential of a global minimal Weierstrass model.

A better way of formulating the conjecture especially if $E$ is no longer defined over $\mathbb{Q}$ but over an arbitrary global field was given Tate. (See for instance conjecture 2.1 in Dokchitser's paper for a formulation). Since there are no global minimal models anymore one has to make either a conjecture that is invariant of the choice of a model or work with the Néron model.