K12a422
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+2 q^2-4 q+6-7 q^{-1} +10 q^{-2} -9 q^{-3} +9 q^{-4} -8 q^{-5} +6 q^{-6} -4 q^{-7} +2 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-6 t^3+10 t^2-11 t+11-11 t^{-1} +10 t^{-2} -6 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+10 z^6+14 z^4+7 z^2+1 }[/math] |
| Determinant | 69 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^4 z^8+a^2 z^8-a^6 z^6+6 a^4 z^6+6 a^2 z^6-z^6-5 a^6 z^4+12 a^4 z^4+12 a^2 z^4-5 z^4-7 a^6 z^2+10 a^4 z^2+11 a^2 z^2-7 z^2-3 a^6+2 a^4+5 a^2-3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{11}-z a^{11}+2 z^4 a^{10}-z^2 a^{10}+3 z^5 a^9-2 z^3 a^9+z a^9+4 z^6 a^8-5 z^4 a^8+2 z^2 a^8+5 z^7 a^7-11 z^5 a^7+7 z^3 a^7-2 z a^7+5 z^8 a^6-14 z^6 a^6+11 z^4 a^6-8 z^2 a^6+3 a^6+4 z^9 a^5-11 z^7 a^5+z^5 a^5+7 z^3 a^5-3 z a^5+3 z^{10} a^4-10 z^8 a^4+4 z^6 a^4+6 z^4 a^4-6 z^2 a^4+2 a^4+z^{11} a^3+z^9 a^3-23 z^7 a^3+44 z^5 a^3-29 z^3 a^3+8 z a^3+5 z^{10} a^2-28 z^8 a^2+50 z^6 a^2-36 z^4 a^2+15 z^2 a^2-5 a^2+z^{11} a-2 z^9 a-14 z^7 a+46 z^5 a-43 z^3 a+13 z a+2 z^{10}-13 z^8+28 z^6-24 z^4+10 z^2-3+z^9 a^{-1} -7 z^7 a^{-1} +17 z^5 a^{-1} -17 z^3 a^{-1} +6 z a^{-1} }[/math] |
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