Adams-Novikov spectral sequence at p = 2

Question

Does anyone know of any computer calculations of the E2-term of the Adams-Novikov spectral sequence at p=2?

I'd love to get my hands on this data.

Answer 1

I don't think anybody knows how to compute this $E_2$-term efficiently (not just at the prime $2$). I would love to be proved wrong on this, of course.

So far the only documented, algorithmic method that has any chance to be computationally succesful seems to be the method described by Zahler in 1969/1970.

You could use my programs to compute the $E_2$-term of the algebraic Novikov spectral sequence

$$\operatorname{Ext}_{EA}(F_2,F_2) \Rightarrow {\operatorname{Ext}}(BP_{\ast},BP_{\ast})$$

where $EA$ is an associated graded of the $2$-primary Steenrod algebra. But of course that's only a very rough approximation to the Novikov $E_2$-term.