K12a1150
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+10 q^4-17 q^3+25 q^2-30 q+31-29 q^{-1} +23 q^{-2} -15 q^{-3} +8 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+23 t^2-41 t+51-41 t^{-1} +23 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-5 z^4-5 z^2+1 }[/math] |
| Determinant | 197 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-7 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +6 z^4+3 a^4 z^2-8 a^2 z^2-5 z^2 a^{-2} +2 z^2 a^{-4} +3 z^2+2 a^4-2 a^2+ a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+6 z^{10} a^{-2} +12 z^{10}+8 a^3 z^9+12 a z^9+13 z^9 a^{-1} +9 z^9 a^{-3} +6 a^4 z^8-6 a^2 z^8+8 z^8 a^{-4} -20 z^8+3 a^5 z^7-20 a^3 z^7-38 a z^7-34 z^7 a^{-1} -15 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-15 a^4 z^6-8 a^2 z^6-17 z^6 a^{-2} -17 z^6 a^{-4} +z^6 a^{-6} +9 z^6-7 a^5 z^5+24 a^3 z^5+44 a z^5+28 z^5 a^{-1} +7 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+15 a^4 z^4+23 a^2 z^4+12 z^4 a^{-2} +12 z^4 a^{-4} -2 z^4 a^{-6} +3 z^4+3 a^5 z^3-15 a^3 z^3-18 a z^3-9 z^3 a^{-1} -5 z^3 a^{-3} +4 z^3 a^{-5} +2 a^6 z^2-10 a^4 z^2-15 a^2 z^2-3 z^2 a^{-2} -5 z^2 a^{-4} +z^2 a^{-6} +3 a^3 z+2 a z+z a^{-3} +2 a^4+2 a^2+ a^{-4} }[/math] |
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