K12a643
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+2 q^3-4 q^2+8 q-11+14 q^{-1} -15 q^{-2} +15 q^{-3} -12 q^{-4} +9 q^{-5} -5 q^{-6} +2 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-13 t^2+21 t-23+21 t^{-1} -13 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+11 z^4+5 z^2+1 }[/math] |
| Determinant | 99 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-3 z^2 a^6-2 a^6+z^6 a^4+3 z^4 a^4+3 z^2 a^4+2 a^4+2 z^6 a^2+7 z^4 a^2+6 z^2 a^2+a^2+z^6+3 z^4+2 z^2+1-z^4 a^{-2} -3 z^2 a^{-2} - a^{-2} }[/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}+3 a^5 z^9-a^3 z^9-2 a z^9+2 z^9 a^{-1} +4 a^6 z^8-2 a^4 z^8-15 a^2 z^8+2 z^8 a^{-2} -7 z^8+3 a^7 z^7-4 a^5 z^7+4 a^3 z^7+4 a z^7-6 z^7 a^{-1} +z^7 a^{-3} +2 a^8 z^6-10 a^6 z^6-a^4 z^6+31 a^2 z^6-9 z^6 a^{-2} +11 z^6+a^9 z^5-5 a^7 z^5-7 a^3 z^5-6 a z^5+2 z^5 a^{-1} -5 z^5 a^{-3} -4 a^8 z^4+15 a^6 z^4+9 a^4 z^4-33 a^2 z^4+12 z^4 a^{-2} -11 z^4-3 a^9 z^3+2 a^7 z^3+9 a^5 z^3+5 a^3 z^3-2 a z^3+4 z^3 a^{-1} +7 z^3 a^{-3} +a^8 z^2-10 a^6 z^2-6 a^4 z^2+11 a^2 z^2-5 z^2 a^{-2} +z^2+2 a^9 z-a^7 z-4 a^5 z+a z-2 z a^{-1} -2 z a^{-3} +2 a^6+2 a^4-a^2+ a^{-2} +1 }[/math] |
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