K12n879
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-5 q^2+11 q-16+22 q^{-1} -24 q^{-2} +23 q^{-3} -19 q^{-4} +13 q^{-5} -7 q^{-6} +2 q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-17 t^2+30 t-35+30 t^{-1} -17 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6-z^4+1 }[/math] |
| Determinant | 143 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+a^4 z^6-4 a^2 z^6+z^6+a^4 z^4-4 a^2 z^4+2 z^4+a^6 z^2-3 a^4 z^2+2 a^2 z^2+a^6-3 a^4+3 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^4 z^{10}+3 a^2 z^{10}+6 a^5 z^9+15 a^3 z^9+9 a z^9+4 a^6 z^8+6 a^4 z^8+12 a^2 z^8+10 z^8+a^7 z^7-8 a^5 z^7-29 a^3 z^7-15 a z^7+5 z^7 a^{-1} +a^6 z^6-14 a^4 z^6-39 a^2 z^6+z^6 a^{-2} -23 z^6+7 a^7 z^5+14 a^5 z^5+16 a^3 z^5-9 z^5 a^{-1} +3 a^8 z^4-2 a^6 z^4+4 a^4 z^4+22 a^2 z^4-z^4 a^{-2} +12 z^4-8 a^7 z^3-13 a^5 z^3-4 a^3 z^3+3 a z^3+2 z^3 a^{-1} -2 a^8 z^2+5 a^4 z^2+3 a^2 z^2+2 a^7 z+4 a^5 z+2 a^3 z-a^6-3 a^4-3 a^2 }[/math] |
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