K12a395
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+16 q^{-1} -23 q^{-2} +28 q^{-3} -28 q^{-4} +27 q^{-5} -21 q^{-6} +14 q^{-7} -8 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-18 t^2+42 t-55+42 t^{-1} -18 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+6 z^4+6 z^2+1 }[/math] |
| Determinant | 183 |
| 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+3 z^2 a^6+a^6+2 z^6 a^4+5 z^4 a^4+6 z^2 a^4+3 a^4+z^6 a^2+z^4 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}+9 z^4 a^{10}-2 z^2 a^{10}+5 z^9 a^9-15 z^7 a^9+14 z^5 a^9-9 z^3 a^9+4 z a^9+5 z^{10} a^8-11 z^8 a^8+5 z^6 a^8-4 z^4 a^8+4 z^2 a^8-2 a^8+2 z^{11} a^7+8 z^9 a^7-39 z^7 a^7+52 z^5 a^7-35 z^3 a^7+9 z a^7+12 z^{10} a^6-28 z^8 a^6+17 z^6 a^6+3 z^4 a^6-5 z^2 a^6-a^6+2 z^{11} a^5+14 z^9 a^5-48 z^7 a^5+53 z^5 a^5-22 z^3 a^5+3 z a^5+7 z^{10} a^4-3 z^8 a^4-19 z^6 a^4+31 z^4 a^4-16 z^2 a^4+3 a^4+11 z^9 a^3-17 z^7 a^3+7 z^5 a^3+4 z^3 a^3-z a^3+11 z^8 a^2-17 z^6 a^2+10 z^4 a^2-4 z^2 a^2+a^2+8 z^7 a-11 z^5 a+4 z^3 a-z a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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