K12a928
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-14 q^3+27 q^2-38 q+47-50 q^{-1} +46 q^{-2} -37 q^{-3} +25 q^{-4} -13 q^{-5} +5 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+31 t^2-69 t+91-69 t^{-1} +31 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^4-z^2+1 }[/math] |
| Determinant | 309 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +4 z^6+3 a^4 z^4-7 a^2 z^4-2 z^4 a^{-2} +9 z^4-a^6 z^2+3 a^4 z^2-7 a^2 z^2-3 z^2 a^{-2} +7 z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a^3 z^{11}+5 a z^{11}+12 a^4 z^{10}+31 a^2 z^{10}+19 z^{10}+11 a^5 z^9+25 a^3 z^9+44 a z^9+30 z^9 a^{-1} +5 a^6 z^8-17 a^4 z^8-50 a^2 z^8+26 z^8 a^{-2} -2 z^8+a^7 z^7-27 a^5 z^7-92 a^3 z^7-126 a z^7-48 z^7 a^{-1} +14 z^7 a^{-3} -12 a^6 z^6-12 a^4 z^6-15 a^2 z^6-38 z^6 a^{-2} +5 z^6 a^{-4} -58 z^6-2 a^7 z^5+23 a^5 z^5+85 a^3 z^5+99 a z^5+27 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +10 a^6 z^4+26 a^4 z^4+44 a^2 z^4+25 z^4 a^{-2} -z^4 a^{-4} +54 z^4+a^7 z^3-8 a^5 z^3-30 a^3 z^3-34 a z^3-9 z^3 a^{-1} +4 z^3 a^{-3} -3 a^6 z^2-10 a^4 z^2-18 a^2 z^2-8 z^2 a^{-2} -19 z^2+a^5 z+5 a^3 z+6 a z+2 z a^{-1} +a^4+2 a^2+2 }[/math] |
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