K12a149
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-17 q^6+24 q^5-29 q^4+32 q^3-29 q^2+24 q-16+9 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-22 t^2+43 t-53+43 t^{-1} -22 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+2 z^2+1 }[/math] |
| Determinant | 199 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +3 z^6 a^{-4} +z^6-11 z^4 a^{-2} +11 z^4 a^{-4} -3 z^4 a^{-6} +3 z^4-10 z^2 a^{-2} +15 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} +3 z^2-3 a^{-2} +7 a^{-4} -5 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +4 z^{10} a^{-2} +8 z^{10} a^{-4} +4 z^{10} a^{-6} +7 z^9 a^{-1} +16 z^9 a^{-3} +16 z^9 a^{-5} +7 z^9 a^{-7} +10 z^8 a^{-2} +7 z^8 a^{-4} +11 z^8 a^{-6} +7 z^8 a^{-8} +7 z^8+4 a z^7-6 z^7 a^{-1} -28 z^7 a^{-3} -26 z^7 a^{-5} -4 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-36 z^6 a^{-2} -45 z^6 a^{-4} -38 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} -14 z^6-9 a z^5-9 z^5 a^{-1} +6 z^5 a^{-3} -z^5 a^{-5} -16 z^5 a^{-7} -9 z^5 a^{-9} -2 a^2 z^4+35 z^4 a^{-2} +50 z^4 a^{-4} +35 z^4 a^{-6} +7 z^4 a^{-8} -2 z^4 a^{-10} +9 z^4+6 a z^3+11 z^3 a^{-1} +11 z^3 a^{-3} +19 z^3 a^{-5} +20 z^3 a^{-7} +7 z^3 a^{-9} +a^2 z^2-16 z^2 a^{-2} -26 z^2 a^{-4} -17 z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} -3 z^2-a z-3 z a^{-1} -5 z a^{-3} -9 z a^{-5} -8 z a^{-7} -2 z a^{-9} +3 a^{-2} +7 a^{-4} +5 a^{-6} + a^{-8} +1 }[/math] |
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