K12a959
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+18 q^{-1} -26 q^{-2} +32 q^{-3} -34 q^{-4} +32 q^{-5} -26 q^{-6} +18 q^{-7} -10 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-21 t^2+50 t-65+50 t^{-1} -21 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+3 z^4+2 z^2+1 }[/math] |
| Determinant | 215 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-z^2 a^8-a^8+z^6 a^6+z^4 a^6+2 z^2 a^6+2 a^6+2 z^6 a^4+3 z^4 a^4-2 a^4+z^6 a^2+z^4 a^2+2 z^2 a^2+2 a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-3 z^5 a^{11}+2 z^3 a^{11}+4 z^8 a^{10}-12 z^6 a^{10}+10 z^4 a^{10}-2 z^2 a^{10}+8 z^9 a^9-25 z^7 a^9+26 z^5 a^9-13 z^3 a^9+4 z a^9+8 z^{10} a^8-19 z^8 a^8+12 z^6 a^8-6 z^4 a^8+4 z^2 a^8-a^8+3 z^{11} a^7+11 z^9 a^7-51 z^7 a^7+60 z^5 a^7-35 z^3 a^7+8 z a^7+17 z^{10} a^6-40 z^8 a^6+33 z^6 a^6-21 z^4 a^6+9 z^2 a^6-2 a^6+3 z^{11} a^5+16 z^9 a^5-52 z^7 a^5+53 z^5 a^5-28 z^3 a^5+6 z a^5+9 z^{10} a^4-5 z^8 a^4-11 z^6 a^4+7 z^4 a^4+4 z^2 a^4-2 a^4+13 z^9 a^3-19 z^7 a^3+12 z^5 a^3-4 z^3 a^3+2 z a^3+12 z^8 a^2-16 z^6 a^2+7 z^4 a^2+3 z^2 a^2-2 a^2+8 z^7 a-9 z^5 a+3 z^3 a+4 z^6-5 z^4+2 z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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