K12a244
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-13+22 q^{-1} -30 q^{-2} +38 q^{-3} -38 q^{-4} +35 q^{-5} -28 q^{-6} +18 q^{-7} -10 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^3-24 t^2+56 t-73+56 t^{-1} -24 t^{-2} +5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^6+6 z^4+5 z^2+1 }[/math] |
| Determinant | 243 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-z^2 a^8+z^6 a^6-3 z^2 a^6-4 a^6+3 z^6 a^4+9 z^4 a^4+13 z^2 a^4+7 a^4+z^6 a^2-z^4 a^2-4 z^2 a^2-2 a^2-z^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-3 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+4 z^8 a^{10}-12 z^6 a^{10}+12 z^4 a^{10}-4 z^2 a^{10}+7 z^9 a^9-18 z^7 a^9+14 z^5 a^9-3 z^3 a^9+6 z^{10} a^8-3 z^8 a^8-23 z^6 a^8+28 z^4 a^8-8 z^2 a^8+2 z^{11} a^7+19 z^9 a^7-57 z^7 a^7+43 z^5 a^7-5 z^3 a^7-4 z a^7+15 z^{10} a^6-9 z^8 a^6-47 z^6 a^6+56 z^4 a^6-20 z^2 a^6+4 a^6+2 z^{11} a^5+30 z^9 a^5-68 z^7 a^5+31 z^5 a^5+10 z^3 a^5-9 z a^5+9 z^{10} a^4+18 z^8 a^4-71 z^6 a^4+60 z^4 a^4-23 z^2 a^4+7 a^4+18 z^9 a^3-17 z^7 a^3-10 z^5 a^3+14 z^3 a^3-6 z a^3+20 z^8 a^2-30 z^6 a^2+18 z^4 a^2-7 z^2 a^2+2 a^2+13 z^7 a-14 z^5 a+5 z^3 a-2 z a+5 z^6-2 z^4+z^5 a^{-1} }[/math] |
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