Re: Solvable septic (parametric)


Peter L. Montgomery wrote:
> In article <de1thm$ev4$1@xxxxxxxxxxxxxxxxxxxxxxxxx>
> titus_piezas@xxxxxxxxx writes:

(snip)

How feasible is it to find ALL solvable septics with constant term +/-1
and the other coefficients' absolute values are < 10 (or better, < 15)?
There _might_ be a parametric form where the coefficients are only in a
linear progression and it might be possible to see the pattern given
enough data.

Some septics with small coefficients are Weber class polynomials, the
coefficient list of the smallest being (-1 as the constant term):

{1, -2, -1, 1, 1, 1, -1, -1}
{1, -3, -1, -3, 0, -1, -1, -1}
{1, -5, 0, 1, -4, -1, 0, -1}

for fundamental discriminants 71, 151, 223, respectively.

It's hard to see any pattern from just 3 examples. Anybody has the
resources to find more?

-Titus

.