Computing the rank and torsion of the elliptic curve y^2=x^3+x+1 over \QQ.
Need to compute the j-invariant of the elliptic curve over \CC.
Computing the number of points for the (non-elliptic, singular) curve over extensions of F_2. I will label this integer sequence n_{2,x^3+x+1}.
Can compute the number of points of the elliptic curve over F_7, F_49, i.e. extensions of all degree.
Computes the Zeta function over F_7 to verify the Weil conjectures using explicit formula factoring a quadratic polynomial with number of points a_p.
Looking for more information on the curve y^2=x^3+x+1 over the algebraic closure of F_2, \overline{F_2}.
Acknowledgements: Ezra Brown, Joe Silverman, Robert Pollack, Angus McAndrew, Roderic Corominas, and Tim Kohl.