K12a1242
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-2 q^{10}+3 q^9-4 q^8+5 q^7-6 q^6+6 q^5-6 q^4+5 q^3-4 q^2+3 q-1+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+5 t^3-6 t^2+7 t-7+7 t^{-1} -6 t^{-2} +5 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-11 z^6-16 z^4-4 z^2+1 }[/math] |
| Determinant | 47 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-4} -z^8 a^{-6} +z^6 a^{-2} -7 z^6 a^{-4} -6 z^6 a^{-6} +z^6 a^{-8} +6 z^4 a^{-2} -17 z^4 a^{-4} -10 z^4 a^{-6} +5 z^4 a^{-8} +11 z^2 a^{-2} -18 z^2 a^{-4} -3 z^2 a^{-6} +6 z^2 a^{-8} +6 a^{-2} -8 a^{-4} +2 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +z^{10} a^{-2} +4 z^{10} a^{-4} +3 z^{10} a^{-6} -7 z^9 a^{-3} -2 z^9 a^{-5} +5 z^9 a^{-7} -9 z^8 a^{-2} -30 z^8 a^{-4} -15 z^8 a^{-6} +6 z^8 a^{-8} +15 z^7 a^{-3} -16 z^7 a^{-5} -25 z^7 a^{-7} +6 z^7 a^{-9} +30 z^6 a^{-2} +79 z^6 a^{-4} +18 z^6 a^{-6} -26 z^6 a^{-8} +5 z^6 a^{-10} -7 z^5 a^{-3} +53 z^5 a^{-5} +35 z^5 a^{-7} -21 z^5 a^{-9} +4 z^5 a^{-11} -45 z^4 a^{-2} -89 z^4 a^{-4} +29 z^4 a^{-8} -12 z^4 a^{-10} +3 z^4 a^{-12} -8 z^3 a^{-3} -47 z^3 a^{-5} -15 z^3 a^{-7} +16 z^3 a^{-9} -6 z^3 a^{-11} +2 z^3 a^{-13} +29 z^2 a^{-2} +43 z^2 a^{-4} -z^2 a^{-6} -9 z^2 a^{-8} +3 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} +5 z a^{-3} +11 z a^{-5} +3 z a^{-7} -3 z a^{-9} -6 a^{-2} -8 a^{-4} -2 a^{-6} + a^{-8} }[/math] |
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