K12a907
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+4 q^{10}-10 q^9+18 q^8-27 q^7+33 q^6-35 q^5+34 q^4-27 q^3+19 q^2-11 q+5- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+29 t^2-45 t+51-45 t^{-1} +29 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+3 z^4+4 z^2+1 }[/math] |
| Determinant | 225 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +3 z^6 a^{-4} +4 z^6 a^{-6} -z^6 a^{-8} -2 z^4 a^{-2} +z^4 a^{-4} +7 z^4 a^{-6} -3 z^4 a^{-8} +z^2 a^{-2} -2 z^2 a^{-4} +8 z^2 a^{-6} -3 z^2 a^{-8} + a^{-2} - a^{-4} +3 a^{-6} -2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-5} +4 z^{11} a^{-7} +10 z^{10} a^{-4} +21 z^{10} a^{-6} +11 z^{10} a^{-8} +10 z^9 a^{-3} +9 z^9 a^{-5} +14 z^9 a^{-7} +15 z^9 a^{-9} +5 z^8 a^{-2} -26 z^8 a^{-4} -58 z^8 a^{-6} -13 z^8 a^{-8} +14 z^8 a^{-10} +z^7 a^{-1} -31 z^7 a^{-3} -53 z^7 a^{-5} -56 z^7 a^{-7} -26 z^7 a^{-9} +9 z^7 a^{-11} -14 z^6 a^{-2} +17 z^6 a^{-4} +56 z^6 a^{-6} -3 z^6 a^{-8} -24 z^6 a^{-10} +4 z^6 a^{-12} -2 z^5 a^{-1} +26 z^5 a^{-3} +57 z^5 a^{-5} +59 z^5 a^{-7} +17 z^5 a^{-9} -12 z^5 a^{-11} +z^5 a^{-13} +8 z^4 a^{-2} -6 z^4 a^{-4} -28 z^4 a^{-6} +8 z^4 a^{-8} +18 z^4 a^{-10} -4 z^4 a^{-12} -5 z^3 a^{-3} -19 z^3 a^{-5} -23 z^3 a^{-7} -2 z^3 a^{-9} +6 z^3 a^{-11} -z^3 a^{-13} +z^2 a^{-2} +4 z^2 a^{-4} +9 z^2 a^{-6} +z^2 a^{-8} -5 z^2 a^{-10} +2 z a^{-7} -2 z a^{-11} - a^{-2} - a^{-4} -3 a^{-6} -2 a^{-8} }[/math] |
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