K12a1190
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-13 q^6+23 q^5-34 q^4+42 q^3-44 q^2+42 q-33+23 q^{-1} -13 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-31 t^2+61 t-75+61 t^{-1} -31 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+3 z^4+2 z^2+1 }[/math] |
| Determinant | 279 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -3 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-3 z^4 a^{-2} +4 z^4 a^{-4} -z^4 a^{-6} +4 z^4-a^2 z^2+2 z^2 a^{-2} +z^2 a^{-4} -z^2 a^{-6} +z^2+4 a^{-2} -2 a^{-4} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 z^{11} a^{-1} +5 z^{11} a^{-3} +28 z^{10} a^{-2} +16 z^{10} a^{-4} +12 z^{10}+11 a z^9+17 z^9 a^{-1} +29 z^9 a^{-3} +23 z^9 a^{-5} +5 a^2 z^8-60 z^8 a^{-2} -10 z^8 a^{-4} +21 z^8 a^{-6} -24 z^8+a^3 z^7-29 a z^7-76 z^7 a^{-1} -93 z^7 a^{-3} -34 z^7 a^{-5} +13 z^7 a^{-7} -12 a^2 z^6+27 z^6 a^{-2} -23 z^6 a^{-4} -29 z^6 a^{-6} +5 z^6 a^{-8} +4 z^6-2 a^3 z^5+23 a z^5+77 z^5 a^{-1} +83 z^5 a^{-3} +17 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +8 a^2 z^4+3 z^4 a^{-2} +18 z^4 a^{-4} +14 z^4 a^{-6} -2 z^4 a^{-8} +9 z^4+a^3 z^3-8 a z^3-30 z^3 a^{-1} -34 z^3 a^{-3} -9 z^3 a^{-5} +4 z^3 a^{-7} -2 a^2 z^2+3 z^2 a^{-2} -z^2 a^{-4} -3 z^2 a^{-6} -z^2+2 a z+6 z a^{-1} +8 z a^{-3} +4 z a^{-5} -4 a^{-2} -2 a^{-4} -1 }[/math] |
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