K12a362
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+6-14 q^{-1} +24 q^{-2} -33 q^{-3} +40 q^{-4} -41 q^{-5} +38 q^{-6} -30 q^{-7} +19 q^{-8} -10 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+31 t^2-56 t+67-56 t^{-1} +31 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-3 z^4+3 z^2+1 }[/math] |
| Determinant | 261 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^{10}-a^{10}+3 z^4 a^8+6 z^2 a^8+2 a^8-3 z^6 a^6-8 z^4 a^6-6 z^2 a^6-2 a^6+z^8 a^4+3 z^6 a^4+3 z^4 a^4+2 z^2 a^4+a^4-z^6 a^2-z^4 a^2+2 z^2 a^2+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+9 z^7 a^{11}-11 z^5 a^{11}+7 z^3 a^{11}-2 z a^{11}+14 z^8 a^{10}-19 z^6 a^{10}+13 z^4 a^{10}-4 z^2 a^{10}+a^{10}+16 z^9 a^9-21 z^7 a^9+7 z^5 a^9+5 z^3 a^9-z a^9+12 z^{10} a^8-4 z^8 a^8-29 z^6 a^8+35 z^4 a^8-14 z^2 a^8+2 a^8+4 z^{11} a^7+26 z^9 a^7-81 z^7 a^7+68 z^5 a^7-20 z^3 a^7+z a^7+24 z^{10} a^6-43 z^8 a^6-6 z^6 a^6+34 z^4 a^6-17 z^2 a^6+2 a^6+4 z^{11} a^5+23 z^9 a^5-86 z^7 a^5+73 z^5 a^5-19 z^3 a^5+12 z^{10} a^4-19 z^8 a^4-13 z^6 a^4+22 z^4 a^4-6 z^2 a^4+a^4+13 z^9 a^3-34 z^7 a^3+23 z^5 a^3-2 z^3 a^3+6 z^8 a^2-13 z^6 a^2+6 z^4 a^2+2 z^2 a^2-a^2+z^7 a-z^5 a }[/math] |
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