71 knot
# 71 knot

In knot theory, the $7_1$ knot, also known as the septoil knot, the septafoil knot, or the (7, 2)-torus knot, is one of seven prime knots with crossing number seven. It is the simplest torus knot after the trefoil and cinquefoil.

## Properties

The $7_1$ knot is invertible but not amphichiral. Its Alexander polynomial is

    $\Delta (t)=t^{3}-t^{2}+t-1+t^{-1}-t^{-2}+t^{-3},\,$

its Conway polynomial is

    $\nabla (z)=z^{6}+5z^{4}+6z^{2}+1,\,$

and its Jones polynomial is

    $V(q)=q^{-3}+q^{-5}-q^{-6}+q^{-7}-q^{-8}+q^{-9}-q^{-10}.\,$
