K12a1095
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+3 q^5-5 q^4+8 q^3-11 q^2+13 q-14+14 q^{-1} -11 q^{-2} +9 q^{-3} -6 q^{-4} +3 q^{-5} - q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-12 t^2+22 t-25+22 t^{-1} -12 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+6 z^4+z^2+1 }[/math] |
| Determinant | 99 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^6+z^6 a^{-2} +z^6-a^4 z^4+3 a^2 z^4+3 z^4 a^{-2} -z^4 a^{-4} +2 z^4-2 a^4 z^2+3 a^2 z^2+2 z^2 a^{-2} -2 z^2 a^{-4} -a^4+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +9 z^{10} a^{-2} +3 z^{10} a^{-4} +6 z^{10}+9 a z^9+z^9 a^{-1} -7 z^9 a^{-3} +z^9 a^{-5} +10 a^2 z^8-49 z^8 a^{-2} -19 z^8 a^{-4} -20 z^8+10 a^3 z^7-29 a z^7-39 z^7 a^{-1} -6 z^7 a^{-3} -6 z^7 a^{-5} +9 a^4 z^6-24 a^2 z^6+83 z^6 a^{-2} +40 z^6 a^{-4} +10 z^6+6 a^5 z^5-18 a^3 z^5+23 a z^5+74 z^5 a^{-1} +39 z^5 a^{-3} +12 z^5 a^{-5} +3 a^6 z^4-13 a^4 z^4+8 a^2 z^4-48 z^4 a^{-2} -32 z^4 a^{-4} +8 z^4+a^7 z^3-4 a^5 z^3+3 a^3 z^3-9 a z^3-43 z^3 a^{-1} -36 z^3 a^{-3} -10 z^3 a^{-5} +5 a^4 z^2+2 a^2 z^2+7 z^2 a^{-2} +7 z^2 a^{-4} -3 z^2+a^5 z+a^3 z+3 a z+9 z a^{-1} +9 z a^{-3} +3 z a^{-5} -a^4-2 a^2 }[/math] |
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