K12a608
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+17 q^{-1} -24 q^{-2} +29 q^{-3} -30 q^{-4} +28 q^{-5} -22 q^{-6} +15 q^{-7} -8 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-19 t^2+44 t-57+44 t^{-1} -19 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+5 z^4+4 z^2+1 }[/math] |
| Determinant | 191 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-2 a^8+z^6 a^6+2 z^4 a^6+4 z^2 a^6+3 a^6+2 z^6 a^4+4 z^4 a^4+2 z^2 a^4-a^4+z^6 a^2+z^4 a^2+z^2 a^2+a^2-z^4-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}-10 z^6 a^{10}+10 z^4 a^{10}-3 z^2 a^{10}+5 z^9 a^9-14 z^7 a^9+11 z^5 a^9-3 z^3 a^9+z a^9+5 z^{10} a^8-10 z^8 a^8+5 z^6 a^8-7 z^4 a^8+8 z^2 a^8-2 a^8+2 z^{11} a^7+8 z^9 a^7-32 z^7 a^7+34 z^5 a^7-20 z^3 a^7+5 z a^7+12 z^{10} a^6-26 z^8 a^6+24 z^6 a^6-24 z^4 a^6+14 z^2 a^6-3 a^6+2 z^{11} a^5+14 z^9 a^5-39 z^7 a^5+36 z^5 a^5-18 z^3 a^5+3 z a^5+7 z^{10} a^4-2 z^8 a^4-9 z^6 a^4+3 z^4 a^4+3 z^2 a^4-a^4+11 z^9 a^3-14 z^7 a^3+6 z^5 a^3-z^3 a^3+z a^3+11 z^8 a^2-14 z^6 a^2+5 z^4 a^2+2 z^2 a^2-a^2+8 z^7 a-10 z^5 a+4 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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