K12a280
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-16 q^6+23 q^5-29 q^4+31 q^3-28 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+42 t-51+42 t^{-1} -22 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+z^2+1 }[/math] |
| Determinant | 195 |
| 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} +14 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} +3 z^2-2 a^{-2} +5 a^{-4} -4 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} +6 z^8 a^{-4} +10 z^8 a^{-6} +7 z^8 a^{-8} +7 z^8+4 a z^7-6 z^7 a^{-1} -31 z^7 a^{-3} -31 z^7 a^{-5} -6 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-39 z^6 a^{-2} -49 z^6 a^{-4} -40 z^6 a^{-6} -14 z^6 a^{-8} +z^6 a^{-10} -14 z^6-9 a z^5-10 z^5 a^{-1} +11 z^5 a^{-3} +9 z^5 a^{-5} -12 z^5 a^{-7} -9 z^5 a^{-9} -2 a^2 z^4+41 z^4 a^{-2} +62 z^4 a^{-4} +42 z^4 a^{-6} +8 z^4 a^{-8} -2 z^4 a^{-10} +9 z^4+6 a z^3+11 z^3 a^{-1} +9 z^3 a^{-3} +14 z^3 a^{-5} +16 z^3 a^{-7} +6 z^3 a^{-9} +a^2 z^2-20 z^2 a^{-2} -30 z^2 a^{-4} -19 z^2 a^{-6} -3 z^2 a^{-8} +z^2 a^{-10} -4 z^2-a z-3 z a^{-1} -4 z a^{-3} -6 z a^{-5} -6 z a^{-7} -2 z a^{-9} +2 a^{-2} +5 a^{-4} +4 a^{-6} + a^{-8} +1 }[/math] |
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