K12a153
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-6+10 q^{-1} -13 q^{-2} +16 q^{-3} -16 q^{-4} +15 q^{-5} -11 q^{-6} +8 q^{-7} -5 q^{-8} +2 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-11 t^2+24 t-31+24 t^{-1} -11 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+7 z^4+7 z^2+1 }[/math] |
| Determinant | 107 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-3 z^2 a^8-3 a^8+z^6 a^6+4 z^4 a^6+7 z^2 a^6+4 a^6+z^6 a^4+2 z^4 a^4+z^2 a^4-a^4+z^6 a^2+3 z^4 a^2+4 z^2 a^2+2 a^2-z^4-2 z^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-5 z^5 a^{11}+7 z^3 a^{11}-3 z a^{11}+2 z^8 a^{10}-8 z^6 a^{10}+7 z^4 a^{10}-z^2 a^{10}+3 z^9 a^9-12 z^7 a^9+14 z^5 a^9-10 z^3 a^9+4 z a^9+3 z^{10} a^8-12 z^8 a^8+18 z^6 a^8-20 z^4 a^8+12 z^2 a^8-3 a^8+z^{11} a^7+3 z^9 a^7-27 z^7 a^7+53 z^5 a^7-44 z^3 a^7+12 z a^7+6 z^{10} a^6-24 z^8 a^6+37 z^6 a^6-26 z^4 a^6+12 z^2 a^6-4 a^6+z^{11} a^5+4 z^9 a^5-25 z^7 a^5+46 z^5 a^5-29 z^3 a^5+6 z a^5+3 z^{10} a^4-6 z^8 a^4+5 z^6 a^4+z^4 a^4+2 z^2 a^4-a^4+4 z^9 a^3-7 z^7 a^3+6 z^5 a^3-2 z^3 a^3+z a^3+4 z^8 a^2-3 z^6 a^2-6 z^4 a^2+6 z^2 a^2-2 a^2+4 z^7 a-5 z^5 a-2 z^3 a+z a+3 z^6-6 z^4+3 z^2-1+z^5 a^{-1} -2 z^3 a^{-1} +z a^{-1} }[/math] |
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