K12a452
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-22 q^3+32 q^2-38 q+41-37 q^{-1} +30 q^{-2} -20 q^{-3} +10 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+28 t^2-55 t+69-55 t^{-1} +28 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^2+1 }[/math] |
| Determinant | 253 |
| 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^4-5 z^4 a^{-2} +z^4 a^{-4} +9 z^4+2 a^4 z^2-8 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +11 z^2+a^4-4 a^2-2 a^{-2} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +9 a^2 z^{10}+10 z^{10} a^{-2} +19 z^{10}+11 a^3 z^9+22 a z^9+25 z^9 a^{-1} +14 z^9 a^{-3} +8 a^4 z^8-4 a^2 z^8+11 z^8 a^{-4} -23 z^8+4 a^5 z^7-18 a^3 z^7-62 a z^7-67 z^7 a^{-1} -22 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-14 a^4 z^6-18 a^2 z^6-35 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} -17 z^6-8 a^5 z^5+10 a^3 z^5+58 a z^5+53 z^5 a^{-1} +5 z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+8 a^4 z^4+26 a^2 z^4+36 z^4 a^{-2} +11 z^4 a^{-4} -z^4 a^{-6} +40 z^4+5 a^5 z^3-a^3 z^3-19 a z^3-13 z^3 a^{-1} +3 z^3 a^{-3} +3 z^3 a^{-5} +a^6 z^2-3 a^4 z^2-16 a^2 z^2-14 z^2 a^{-2} -3 z^2 a^{-4} -23 z^2-a^5 z-2 a^3 z-a z-z a^{-1} -z a^{-3} +a^4+4 a^2+2 a^{-2} +6 }[/math] |
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