K12a1157
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-2 q^{10}+3 q^9-4 q^8+4 q^7-5 q^6+5 q^5-4 q^4+4 q^3-3 q^2+2 q-1+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+5 t^3-5 t^2+5 t-5+5 t^{-1} -5 t^{-2} +5 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-11 z^6-15 z^4-2 z^2+1 }[/math] |
| Determinant | 39 |
| 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} -16 z^4 a^{-4} -10 z^4 a^{-6} +5 z^4 a^{-8} +10 z^2 a^{-2} -14 z^2 a^{-4} -4 z^2 a^{-6} +6 z^2 a^{-8} +4 a^{-2} -4 a^{-4} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +z^{10} a^{-2} +3 z^{10} a^{-4} +2 z^{10} a^{-6} -8 z^9 a^{-3} -5 z^9 a^{-5} +3 z^9 a^{-7} -9 z^8 a^{-2} -23 z^8 a^{-4} -10 z^8 a^{-6} +4 z^8 a^{-8} +22 z^7 a^{-3} +4 z^7 a^{-5} -14 z^7 a^{-7} +4 z^7 a^{-9} +29 z^6 a^{-2} +61 z^6 a^{-4} +11 z^6 a^{-6} -17 z^6 a^{-8} +4 z^6 a^{-10} -24 z^5 a^{-3} +8 z^5 a^{-5} +16 z^5 a^{-7} -12 z^5 a^{-9} +4 z^5 a^{-11} -40 z^4 a^{-2} -67 z^4 a^{-4} +4 z^4 a^{-6} +19 z^4 a^{-8} -9 z^4 a^{-10} +3 z^4 a^{-12} +8 z^3 a^{-3} -8 z^3 a^{-5} -2 z^3 a^{-7} +5 z^3 a^{-9} -7 z^3 a^{-11} +2 z^3 a^{-13} +22 z^2 a^{-2} +29 z^2 a^{-4} -5 z^2 a^{-6} -7 z^2 a^{-8} +2 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} +z a^{-3} +z a^{-5} -z a^{-7} +z a^{-9} +2 z a^{-11} -4 a^{-2} -4 a^{-4} + a^{-8} }[/math] |
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