K12a74
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+11 q-20+30 q^{-1} -38 q^{-2} +41 q^{-3} -38 q^{-4} +32 q^{-5} -22 q^{-6} +12 q^{-7} -5 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-26 t^2+57 t-73+57 t^{-1} -26 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-4 z^4+1 }[/math] |
| Determinant | 255 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8-3 z^4 a^6-4 z^2 a^6-2 a^6+3 z^6 a^4+9 z^4 a^4+12 z^2 a^4+6 a^4-z^8 a^2-5 z^6 a^2-13 z^4 a^2-14 z^2 a^2-6 a^2+z^6+3 z^4+5 z^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^5 z^{11}+2 a^3 z^{11}+8 a^6 z^{10}+15 a^4 z^{10}+7 a^2 z^{10}+13 a^7 z^9+28 a^5 z^9+26 a^3 z^9+11 a z^9+11 a^8 z^8+12 a^6 z^8+4 a^4 z^8+12 a^2 z^8+9 z^8+5 a^9 z^7-16 a^7 z^7-56 a^5 z^7-54 a^3 z^7-15 a z^7+4 z^7 a^{-1} +a^{10} z^6-20 a^8 z^6-53 a^6 z^6-67 a^4 z^6-54 a^2 z^6+z^6 a^{-2} -18 z^6-8 a^9 z^5-3 a^7 z^5+21 a^5 z^5+27 a^3 z^5+4 a z^5-7 z^5 a^{-1} -a^{10} z^4+13 a^8 z^4+45 a^6 z^4+73 a^4 z^4+61 a^2 z^4-2 z^4 a^{-2} +17 z^4+4 a^9 z^3+8 a^7 z^3+6 a^5 z^3+a^3 z^3+3 a z^3+4 z^3 a^{-1} -3 a^8 z^2-16 a^6 z^2-33 a^4 z^2-31 a^2 z^2+z^2 a^{-2} -10 z^2-2 a^7 z-3 a^5 z-a^3 z-a z-z a^{-1} +2 a^6+6 a^4+6 a^2+3 }[/math] |
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