When doubling a point on an elliptic curve, we use $\lambda$. But the equation I found in my book(Silverman and Tate, Rational Points on Elliptic Curves) isn't the same as the one I found when looking on the internet. Silverman and Tate's definition is this one: $$\lambda=\frac{3x^2+2ax+b}{2y}$$ The one I found on the internet is this one: $$\lambda=\frac{3x^2+a}{2y}$$ I've calculated the example in the book, and I only get the right answer if I use the last one, i.e. the one not from their book. Is $\lambda$ just wrong in the book or is there something I've overlooked? I've looked at the corrections for the book, but this isn't mentioned in there.
EDIT: The formulas for x and y are both places as follows: $$x_r=\lambda^2-2x$$ $$y_r=\lambda(x-x_r)-y$$
The definition of the elliptic curve is this in Silverman and Tate: $$y^2=x^3+bx+c$$ This formula doesn't mention an a, but I'm assuming that a is the one that should be in front of $x^3$, i.e. 1.
The definition from the internet is $$y^2=x^3+ax+b$$