K12a316
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-6 q^5+15 q^4-25 q^3+36 q^2-43 q+45-41 q^{-1} +32 q^{-2} -21 q^{-3} +11 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+29 t^2-62 t+81-62 t^{-1} +29 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^4-2 z^2+1 }[/math] |
| Determinant | 281 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-6 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +9 z^4+2 a^4 z^2-9 a^2 z^2-3 z^2 a^{-2} +8 z^2+2 a^4-4 a^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +9 a^2 z^{10}+12 z^{10} a^{-2} +21 z^{10}+12 a^3 z^9+28 a z^9+35 z^9 a^{-1} +19 z^9 a^{-3} +9 a^4 z^8+5 a^2 z^8+6 z^8 a^{-2} +15 z^8 a^{-4} -13 z^8+4 a^5 z^7-18 a^3 z^7-68 a z^7-82 z^7 a^{-1} -30 z^7 a^{-3} +6 z^7 a^{-5} +a^6 z^6-17 a^4 z^6-41 a^2 z^6-52 z^6 a^{-2} -25 z^6 a^{-4} +z^6 a^{-6} -49 z^6-7 a^5 z^5+10 a^3 z^5+50 a z^5+46 z^5 a^{-1} +7 z^5 a^{-3} -6 z^5 a^{-5} -2 a^6 z^4+15 a^4 z^4+50 a^2 z^4+37 z^4 a^{-2} +9 z^4 a^{-4} +61 z^4+4 a^5 z^3-2 a^3 z^3-11 a z^3-2 z^3 a^{-1} +3 z^3 a^{-3} +a^6 z^2-8 a^4 z^2-25 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} -23 z^2-a^5 z-2 z a^{-1} -z a^{-3} +2 a^4+4 a^2+3 }[/math] |
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