Let $E$ be the elliptic curve over $\mathbb{Q}$ defined by $y^2+y=x^3-x$. Show that the discriminant $\Delta=37$.
Attempt: For an elliptic curve of the form $y^2=x^3+Ax+B$, the discriminant is $4A^3+27B^2$. Completing the square we have $(y+1/2)^2=x^3-x+1/4$. The issue here is that on the LHS we have $y+1/2$ instead of $y$, and also we cannot use the discriminant formula I mentioned since $B\notin\mathbb{Z}$. Is there a way around this?