K12a509
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-18 q^6+26 q^5-33 q^4+35 q^3-32 q^2+27 q-18+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-26 t^2+45 t-53+45 t^{-1} -26 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-6 z^4-z^2+1 }[/math] |
| Determinant | 219 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-6 z^4 a^{-2} -6 z^4 a^{-4} +3 z^4 a^{-6} +3 z^4-3 z^2 a^{-2} -4 z^2 a^{-4} +3 z^2 a^{-6} +3 z^2+ a^{-2} -2 a^{-4} + a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +13 z^{10} a^{-4} +7 z^{10} a^{-6} +9 z^9 a^{-1} +16 z^9 a^{-3} +17 z^9 a^{-5} +10 z^9 a^{-7} +5 z^8 a^{-2} -14 z^8 a^{-4} -3 z^8 a^{-6} +8 z^8 a^{-8} +8 z^8+4 a z^7-11 z^7 a^{-1} -33 z^7 a^{-3} -41 z^7 a^{-5} -19 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-28 z^6 a^{-2} -2 z^6 a^{-4} -8 z^6 a^{-6} -16 z^6 a^{-8} +z^6 a^{-10} -16 z^6-8 a z^5-3 z^5 a^{-1} +16 z^5 a^{-3} +35 z^5 a^{-5} +16 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+23 z^4 a^{-2} +3 z^4 a^{-6} +10 z^4 a^{-8} -2 z^4 a^{-10} +12 z^4+5 a z^3+7 z^3 a^{-1} -z^3 a^{-3} -17 z^3 a^{-5} -10 z^3 a^{-7} +4 z^3 a^{-9} +a^2 z^2-6 z^2 a^{-2} +5 z^2 a^{-4} +2 z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} -5 z^2-a z-2 z a^{-1} +z a^{-3} +5 z a^{-5} +3 z a^{-7} - a^{-2} -2 a^{-4} - a^{-6} +1 }[/math] |
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