K12a366
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+11 q^4-18 q^3+25 q^2-29 q+31-27 q^{-1} +21 q^{-2} -14 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+20 t^2-44 t+57-44 t^{-1} +20 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-4 z^4+1 }[/math] |
| Determinant | 193 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-2 a^2 z^4+z^4 a^{-4} -4 z^4+2 a^4 z^2-3 a^2 z^2+3 z^2 a^{-2} -2 z^2+a^4-2 a^2+2 a^{-2} - a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+7 z^{10} a^{-2} +12 z^{10}+6 a^3 z^9+9 a z^9+14 z^9 a^{-1} +11 z^9 a^{-3} +5 a^4 z^8-5 a^2 z^8-4 z^8 a^{-2} +10 z^8 a^{-4} -24 z^8+3 a^5 z^7-11 a^3 z^7-30 a z^7-42 z^7 a^{-1} -21 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-11 a^4 z^6-3 a^2 z^6-13 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} +18 z^6-8 a^5 z^5+6 a^3 z^5+37 a z^5+41 z^5 a^{-1} +9 z^5 a^{-3} -9 z^5 a^{-5} -3 a^6 z^4+7 a^4 z^4+11 a^2 z^4+8 z^4 a^{-2} +9 z^4 a^{-4} -z^4 a^{-6} -z^4+6 a^5 z^3+a^3 z^3-14 a z^3-15 z^3 a^{-1} -4 z^3 a^{-3} +2 z^3 a^{-5} +2 a^6 z^2-3 a^4 z^2-8 a^2 z^2+2 z^2 a^{-2} -z^2-2 a^5 z-3 a^3 z+2 z a^{-1} +2 z a^{-3} +z a^{-5} +a^4+2 a^2-2 a^{-2} - a^{-4} +1 }[/math] |
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