K12a303
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-8 q^3+13 q^2-19 q+23-23 q^{-1} +22 q^{-2} -17 q^{-3} +12 q^{-4} -7 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+14 t^2-36 t+49-36 t^{-1} +14 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+2 z^4+2 z^2+1 }[/math] |
| Determinant | 153 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+2 z^4 a^4+3 z^2 a^4+a^4-z^6 a^2-z^4 a^2+a^2-z^6-z^4-z^2+2 z^4 a^{-2} +2 z^2 a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+7 a^2 z^{10}+4 z^{10}+4 a^5 z^9+8 a^3 z^9+11 a z^9+7 z^9 a^{-1} +3 a^6 z^8-2 a^4 z^8-11 a^2 z^8+8 z^8 a^{-2} +2 z^8+a^7 z^7-11 a^5 z^7-30 a^3 z^7-33 a z^7-8 z^7 a^{-1} +7 z^7 a^{-3} -11 a^6 z^6-15 a^4 z^6-6 a^2 z^6-11 z^6 a^{-2} +4 z^6 a^{-4} -17 z^6-4 a^7 z^5+5 a^5 z^5+31 a^3 z^5+35 a z^5+z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +12 a^6 z^4+19 a^4 z^4+17 a^2 z^4+4 z^4 a^{-2} -6 z^4 a^{-4} +20 z^4+5 a^7 z^3+2 a^5 z^3-15 a^3 z^3-15 a z^3+2 z^3 a^{-1} +4 z^3 a^{-3} -z^3 a^{-5} -5 a^6 z^2-8 a^4 z^2-7 a^2 z^2-z^2 a^{-2} +z^2 a^{-4} -6 z^2-2 a^7 z-a^5 z+3 a^3 z+3 a z+z a^{-1} +a^6+a^4-a^2 }[/math] |
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