K12a656
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-12+21 q^{-1} -29 q^{-2} +36 q^{-3} -37 q^{-4} +34 q^{-5} -27 q^{-6} +18 q^{-7} -10 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-22 t^2+55 t-73+55 t^{-1} -22 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+2 z^4+3 z^2+1 }[/math] |
| Determinant | 235 |
| 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+a^6+2 z^6 a^4+3 z^4 a^4+2 z^2 a^4+z^6 a^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}+11 z^4 a^{10}-3 z^2 a^{10}+7 z^9 a^9-18 z^7 a^9+12 z^5 a^9-2 z^3 a^9+7 z^{10} a^8-11 z^8 a^8-5 z^6 a^8+9 z^4 a^8-z^2 a^8-a^8+3 z^{11} a^7+12 z^9 a^7-47 z^7 a^7+42 z^5 a^7-12 z^3 a^7+18 z^{10} a^6-35 z^8 a^6+11 z^6 a^6+6 z^4 a^6-a^6+3 z^{11} a^5+23 z^9 a^5-66 z^7 a^5+51 z^5 a^5-10 z^3 a^5-z a^5+11 z^{10} a^4-2 z^8 a^4-27 z^6 a^4+22 z^4 a^4-3 z^2 a^4+18 z^9 a^3-26 z^7 a^3+10 z^5 a^3-z^3 a^3+18 z^8 a^2-26 z^6 a^2+11 z^4 a^2-z^2 a^2-a^2+12 z^7 a-13 z^5 a+2 z^3 a+5 z^6-3 z^4+z^5 a^{-1} }[/math] |
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