K12a582
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-6+11 q^{-1} -15 q^{-2} +19 q^{-3} -20 q^{-4} +19 q^{-5} -15 q^{-6} +11 q^{-7} -7 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-15 t^2+29 t-35+29 t^{-1} -15 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+9 z^4+5 z^2+1 }[/math] |
| Determinant | 131 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-a^8+z^6 a^6+2 z^4 a^6-a^6+2 z^6 a^4+7 z^4 a^4+9 z^2 a^4+4 a^4+z^6 a^2+2 z^4 a^2-a^2-z^4-2 z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-11 z^6 a^{10}+11 z^4 a^{10}-3 z^2 a^{10}+4 z^9 a^9-12 z^7 a^9+7 z^5 a^9+z a^9+3 z^{10} a^8-5 z^8 a^8-4 z^6 a^8+2 z^4 a^8+4 z^2 a^8-a^8+z^{11} a^7+5 z^9 a^7-21 z^7 a^7+22 z^5 a^7-14 z^3 a^7+4 z a^7+6 z^{10} a^6-14 z^8 a^6+10 z^6 a^6-2 z^4 a^6-3 z^2 a^6+a^6+z^{11} a^5+6 z^9 a^5-21 z^7 a^5+27 z^5 a^5-14 z^3 a^5+z a^5+3 z^{10} a^4-13 z^6 a^4+27 z^4 a^4-18 z^2 a^4+4 a^4+5 z^9 a^3-8 z^7 a^3+5 z^5 a^3+3 z^3 a^3-z a^3+6 z^8 a^2-13 z^6 a^2+14 z^4 a^2-6 z^2 a^2+a^2+5 z^7 a-10 z^5 a+6 z^3 a-z a+3 z^6-6 z^4+2 z^2+z^5 a^{-1} -2 z^3 a^{-1} }[/math] |
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