K12n127
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^6+6 q^5-11 q^4+15 q^3-17 q^2+18 q-15+12 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-14 t^2+21 t-23+21 t^{-1} -14 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6+2 z^4+3 z^2+1 }[/math] |
| Determinant | 107 |
| 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^4-9 z^4 a^{-2} +4 z^4 a^{-4} +8 z^4-3 a^2 z^2-8 z^2 a^{-2} +5 z^2 a^{-4} -z^2 a^{-6} +10 z^2-2 a^2-3 a^{-2} +2 a^{-4} - a^{-6} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+4 a z^9+11 z^9 a^{-1} +7 z^9 a^{-3} +3 a^2 z^8+10 z^8 a^{-2} +9 z^8 a^{-4} +4 z^8+a^3 z^7-11 a z^7-31 z^7 a^{-1} -14 z^7 a^{-3} +5 z^7 a^{-5} -11 a^2 z^6-44 z^6 a^{-2} -23 z^6 a^{-4} +z^6 a^{-6} -31 z^6-4 a^3 z^5+4 a z^5+21 z^5 a^{-1} +8 z^5 a^{-3} -5 z^5 a^{-5} +13 a^2 z^4+48 z^4 a^{-2} +29 z^4 a^{-4} +6 z^4 a^{-6} +38 z^4+5 a^3 z^3+5 a z^3-4 z^3 a^{-1} -z^3 a^{-3} +6 z^3 a^{-5} +3 z^3 a^{-7} -7 a^2 z^2-22 z^2 a^{-2} -14 z^2 a^{-4} -5 z^2 a^{-6} -20 z^2-2 a^3 z-3 a z-z a^{-1} -2 z a^{-5} -2 z a^{-7} +2 a^2+3 a^{-2} +2 a^{-4} + a^{-6} +5 }[/math] |
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