K12n173
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^6+7 q^5-12 q^4+17 q^3-20 q^2+20 q-18+14 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-16 t^2+25 t-27+25 t^{-1} -16 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6-z^2+1 }[/math] |
| Determinant | 123 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-10 z^4 a^{-2} +4 z^4 a^{-4} +7 z^4-2 a^2 z^2-11 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +7 z^2-5 a^{-2} +4 a^{-4} - a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{10} a^{-2} +3 z^{10}+6 a z^9+16 z^9 a^{-1} +10 z^9 a^{-3} +4 a^2 z^8+12 z^8 a^{-2} +12 z^8 a^{-4} +4 z^8+a^3 z^7-19 a z^7-50 z^7 a^{-1} -24 z^7 a^{-3} +6 z^7 a^{-5} -14 a^2 z^6-61 z^6 a^{-2} -33 z^6 a^{-4} +z^6 a^{-6} -41 z^6-3 a^3 z^5+16 a z^5+45 z^5 a^{-1} +21 z^5 a^{-3} -5 z^5 a^{-5} +15 a^2 z^4+73 z^4 a^{-2} +44 z^4 a^{-4} +8 z^4 a^{-6} +52 z^4+2 a^3 z^3-5 a z^3-18 z^3 a^{-1} -10 z^3 a^{-3} +4 z^3 a^{-5} +3 z^3 a^{-7} -6 a^2 z^2-35 z^2 a^{-2} -25 z^2 a^{-4} -7 z^2 a^{-6} -23 z^2+a z+4 z a^{-1} +3 z a^{-3} -z a^{-5} -z a^{-7} +5 a^{-2} +4 a^{-4} + a^{-6} +3 }[/math] |
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