Microsoft's Favorite Elliptic Curve

The elliptic curve used in MS-DRM is an elliptic curve over the finite field $k=\mathbb{Z}/p\mathbb{Z}$, where

$$p=785963102379428822376694789446897396207498568951.$$

As Beale Screamer remarks, this modulus has high nerd appeal because in hexadecimal it is

89ABCDEF012345672718281831415926141424F7,

which includes counting in hexadecimal, and digits of $e$, $\pi$, and $\sqrt{2}$. The Microsoft elliptic curve $E$ is

$$y^2 = x^3 + 317689081251325503476317476413827693272746955927x$$

$$\qquad +79052896607878758718120572025718535432100651934.$$

We have

$$\char93 E(k) = 785963102379428822376693024881714957612686157429,$$

and the group $E(k)$ is cyclic with generator

$$B = (771507216262649826170648268565579889907769254176,$$

$$\qquad 390157510246556628525279459266514995562533196655).$$