K12a862
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+17 q^{-1} -23 q^{-2} +28 q^{-3} -29 q^{-4} +26 q^{-5} -21 q^{-6} +14 q^{-7} -7 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-19 t^2+42 t-53+42 t^{-1} -19 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+5 z^4+2 z^2+1 }[/math] |
| Determinant | 183 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-a^8+z^6 a^6+2 z^4 a^6+3 z^2 a^6+2 a^6+2 z^6 a^4+4 z^4 a^4+z^2 a^4-2 a^4+z^6 a^2+z^4 a^2+z^2 a^2+2 a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+4 z^3 a^{11}+3 z^8 a^{10}-11 z^6 a^{10}+12 z^4 a^{10}-4 z^2 a^{10}+5 z^9 a^9-17 z^7 a^9+21 z^5 a^9-15 z^3 a^9+5 z a^9+5 z^{10} a^8-13 z^8 a^8+12 z^6 a^8-8 z^4 a^8+z^2 a^8-a^8+2 z^{11} a^7+7 z^9 a^7-36 z^7 a^7+53 z^5 a^7-41 z^3 a^7+11 z a^7+12 z^{10} a^6-30 z^8 a^6+28 z^6 a^6-15 z^4 a^6+5 z^2 a^6-2 a^6+2 z^{11} a^5+14 z^9 a^5-48 z^7 a^5+57 z^5 a^5-32 z^3 a^5+9 z a^5+7 z^{10} a^4-2 z^8 a^4-20 z^6 a^4+25 z^4 a^4-4 z^2 a^4-2 a^4+12 z^9 a^3-22 z^7 a^3+18 z^5 a^3-7 z^3 a^3+3 z a^3+12 z^8 a^2-21 z^6 a^2+15 z^4 a^2-3 z^2 a^2-2 a^2+8 z^7 a-10 z^5 a+2 z^3 a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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