K12a363
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+5-11 q^{-1} +20 q^{-2} -28 q^{-3} +34 q^{-4} -36 q^{-5} +34 q^{-6} -27 q^{-7} +18 q^{-8} -10 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+27 t^2-49 t+59-49 t^{-1} +27 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^4+3 z^2+1 }[/math] |
| Determinant | 229 |
| 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^6-9 z^4 a^6-8 z^2 a^6-2 a^6+z^8 a^4+4 z^6 a^4+7 z^4 a^4+6 z^2 a^4+a^4-z^6 a^2-2 z^4 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}-12 z^5 a^{11}+8 z^3 a^{11}-2 z a^{11}+13 z^8 a^{10}-18 z^6 a^{10}+13 z^4 a^{10}-5 z^2 a^{10}+a^{10}+13 z^9 a^9-13 z^7 a^9-z^5 a^9+5 z^3 a^9+8 z^{10} a^8+8 z^8 a^8-43 z^6 a^8+41 z^4 a^8-15 z^2 a^8+2 a^8+2 z^{11} a^7+26 z^9 a^7-69 z^7 a^7+56 z^5 a^7-22 z^3 a^7+4 z a^7+15 z^{10} a^6-13 z^8 a^6-41 z^6 a^6+53 z^4 a^6-20 z^2 a^6+2 a^6+2 z^{11} a^5+22 z^9 a^5-72 z^7 a^5+64 z^5 a^5-23 z^3 a^5+3 z a^5+7 z^{10} a^4-3 z^8 a^4-34 z^6 a^4+41 z^4 a^4-13 z^2 a^4+a^4+9 z^9 a^3-24 z^7 a^3+18 z^5 a^3-4 z^3 a^3+z a^3+5 z^8 a^2-14 z^6 a^2+12 z^4 a^2-2 z^2 a^2-a^2+z^7 a-2 z^5 a+z^3 a }[/math] |
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