K12a644
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-6 q^3+10 q^2-14 q+17-17 q^{-1} +16 q^{-2} -12 q^{-3} +9 q^{-4} -5 q^{-5} +2 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 8 t^2-28 t+41-28 t^{-1} +8 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 8 z^4+4 z^2+1 }[/math] |
| Determinant | 113 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+z^4 a^4+3 z^4 a^2+4 z^2 a^2+2 a^2+3 z^4+3 z^2+1+z^4 a^{-2} -z^2 a^{-2} - a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+2 a^4 z^{10}+5 a^2 z^{10}+3 z^{10}+2 a^5 z^9+3 a z^9+5 z^9 a^{-1} +2 a^6 z^8-5 a^4 z^8-17 a^2 z^8+6 z^8 a^{-2} -4 z^8+a^7 z^7-4 a^5 z^7-3 a^3 z^7-14 a z^7-11 z^7 a^{-1} +5 z^7 a^{-3} -8 a^6 z^6+6 a^4 z^6+30 a^2 z^6-15 z^6 a^{-2} +3 z^6 a^{-4} -2 z^6-5 a^7 z^5-5 a^5 z^5+2 a^3 z^5+23 a z^5+9 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +9 a^6 z^4-12 a^4 z^4-30 a^2 z^4+16 z^4 a^{-2} -6 z^4 a^{-4} +13 z^4+8 a^7 z^3+11 a^5 z^3-6 a^3 z^3-14 a z^3+4 z^3 a^{-1} +7 z^3 a^{-3} -2 z^3 a^{-5} -3 a^6 z^2+7 a^4 z^2+11 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} -6 z^2-4 a^7 z-4 a^5 z+2 a^3 z+2 a z-2 z a^{-1} -2 z a^{-3} +a^6-2 a^2+ a^{-2} +1 }[/math] |
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