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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 $$y^2=x^3+ax+b$$

MBrown
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  • Since the first has the extra $b$ maybe for the second the variables have been changed to simplify the form. It would help if you included the preliminary equation forms going with each different version of $\lambda$, one from Silverman's book and the other from one of the internet versions. – coffeemath Sep 17 '14 at 12:20
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    I've tried including the other equations now. – MBrown Sep 17 '14 at 12:56
  • So it looks like if Silverman uses $(b,c)$ exactly where the internet site uses $(a,b)$ then the silverman version of $\lambda$ should be $(3x^2+b)/(2y)$... maybe a typo in the book. – coffeemath Sep 17 '14 at 15:25

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