K12a972
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-4 q^4+9 q^3-15 q^2+22 q-26+28 q^{-1} -27 q^{-2} +22 q^{-3} -15 q^{-4} +9 q^{-5} -4 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-24 t^2+36 t-39+36 t^{-1} -24 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-4 z^4-2 z^2+1 }[/math] |
| Determinant | 183 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-4 a^2 z^6+z^6 a^{-2} -4 z^6+3 a^4 z^4-5 a^2 z^4+3 z^4 a^{-2} -5 z^4+2 a^4 z^2-3 a^2 z^2+2 z^2 a^{-2} -3 z^2+a^4-a^2+ a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +10 a^2 z^{10}+6 z^{10} a^{-2} +16 z^{10}+16 a^3 z^9+14 a z^9+2 z^9 a^{-1} +4 z^9 a^{-3} +17 a^4 z^8-12 a^2 z^8-23 z^8 a^{-2} +z^8 a^{-4} -53 z^8+14 a^5 z^7-31 a^3 z^7-69 a z^7-41 z^7 a^{-1} -17 z^7 a^{-3} +9 a^6 z^6-28 a^4 z^6-22 a^2 z^6+25 z^6 a^{-2} -4 z^6 a^{-4} +44 z^6+4 a^7 z^5-17 a^5 z^5+12 a^3 z^5+70 a z^5+60 z^5 a^{-1} +23 z^5 a^{-3} +a^8 z^4-7 a^6 z^4+12 a^4 z^4+27 a^2 z^4-7 z^4 a^{-2} +5 z^4 a^{-4} -5 z^4-a^7 z^3+6 a^5 z^3-a^3 z^3-21 a z^3-24 z^3 a^{-1} -11 z^3 a^{-3} +2 a^6 z^2-4 a^4 z^2-9 a^2 z^2-2 z^2 a^{-4} -z^2-a^5 z+2 a z+2 z a^{-1} +z a^{-3} +a^4+a^2- a^{-2} }[/math] |
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