K12a1029
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+2 q^4-4 q^3+7 q^2-9 q+12-12 q^{-1} +11 q^{-2} -9 q^{-3} +7 q^{-4} -4 q^{-5} +2 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-6 t^3+10 t^2-14 t+17-14 t^{-1} +10 t^{-2} -6 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+10 z^6+14 z^4+4 z^2+1 }[/math] |
| Determinant | 81 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+6 a^2 z^6-z^6 a^{-2} +6 z^6-5 a^4 z^4+12 a^2 z^4-5 z^4 a^{-2} +12 z^4-7 a^4 z^2+9 a^2 z^2-7 z^2 a^{-2} +9 z^2-2 a^4+2 a^2-2 a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+2 a^4 z^{10}+4 a^2 z^{10}+2 z^{10}+2 a^5 z^9-3 a^3 z^9-2 a z^9+3 z^9 a^{-1} +2 a^6 z^8-9 a^4 z^8-20 a^2 z^8+4 z^8 a^{-2} -5 z^8+a^7 z^7-7 a^5 z^7+4 a^3 z^7-9 z^7 a^{-1} +3 z^7 a^{-3} -9 a^6 z^6+19 a^4 z^6+45 a^2 z^6-15 z^6 a^{-2} +2 z^6 a^{-4} -5 a^7 z^5+5 a^5 z^5-a^3 z^5+6 a z^5+8 z^5 a^{-1} -8 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4-26 a^4 z^4-48 a^2 z^4+23 z^4 a^{-2} -5 z^4 a^{-4} +17 z^4+7 a^7 z^3-9 a^3 z^3-4 a z^3+6 z^3 a^{-1} +5 z^3 a^{-3} -3 z^3 a^{-5} -3 a^6 z^2+13 a^4 z^2+18 a^2 z^2-13 z^2 a^{-2} +z^2 a^{-4} -12 z^2-2 a^7 z+4 a^3 z+a z-3 z a^{-1} -z a^{-3} +z a^{-5} -2 a^4-2 a^2+2 a^{-2} +3 }[/math] |
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