K12a57
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-7 q^3+14 q^2-20 q+26-28 q^{-1} +26 q^{-2} -22 q^{-3} +16 q^{-4} -9 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+17 t^2-41 t+55-41 t^{-1} +17 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-z^4+1 }[/math] |
| Determinant | 177 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+3 z^4 a^4+6 z^2 a^4+4 a^4-2 z^6 a^2-6 z^4 a^2-9 z^2 a^2-5 a^2-z^6+2 z^2+2+2 z^4 a^{-2} +3 z^2 a^{-2} +2 a^{-2} -z^2 a^{-4} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+8 a^2 z^{10}+4 z^{10}+6 a^5 z^9+15 a^3 z^9+16 a z^9+7 z^9 a^{-1} +4 a^6 z^8+3 a^4 z^8+a^2 z^8+7 z^8 a^{-2} +9 z^8+a^7 z^7-15 a^5 z^7-45 a^3 z^7-40 a z^7-6 z^7 a^{-1} +5 z^7 a^{-3} -13 a^6 z^6-39 a^4 z^6-52 a^2 z^6-8 z^6 a^{-2} +3 z^6 a^{-4} -37 z^6-3 a^7 z^5+6 a^5 z^5+31 a^3 z^5+28 a z^5-5 z^5 a^{-3} +z^5 a^{-5} +14 a^6 z^4+49 a^4 z^4+69 a^2 z^4+4 z^4 a^{-2} -5 z^4 a^{-4} +43 z^4+3 a^7 z^3+4 a^5 z^3-5 a^3 z^3-5 a z^3+3 z^3 a^{-1} -2 z^3 a^{-5} -6 a^6 z^2-24 a^4 z^2-34 a^2 z^2+z^2 a^{-2} +3 z^2 a^{-4} -18 z^2-a^7 z-2 a^5 z+a z+z a^{-3} +z a^{-5} +a^6+4 a^4+5 a^2-2 a^{-2} - a^{-4} +2 }[/math] |
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