K12a242
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-11 q^6+18 q^5-25 q^4+29 q^3-30 q^2+27 q-20+14 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-22 t^2+41 t-49+41 t^{-1} -22 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+1 }[/math] |
| Determinant | 191 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-12 z^4 a^{-2} +6 z^4 a^{-4} -z^4 a^{-6} +8 z^4-3 a^2 z^2-14 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +12 z^2-2 a^2-6 a^{-2} +2 a^{-4} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +5 z^{10} a^{-4} +3 z^{10}+4 a z^9+11 z^9 a^{-1} +18 z^9 a^{-3} +11 z^9 a^{-5} +3 a^2 z^8-z^8 a^{-2} +14 z^8 a^{-4} +14 z^8 a^{-6} +2 z^8+a^3 z^7-9 a z^7-29 z^7 a^{-1} -35 z^7 a^{-3} -5 z^7 a^{-5} +11 z^7 a^{-7} -11 a^2 z^6-34 z^6 a^{-2} -42 z^6 a^{-4} -18 z^6 a^{-6} +5 z^6 a^{-8} -26 z^6-4 a^3 z^5+14 z^5 a^{-1} +9 z^5 a^{-3} -16 z^5 a^{-5} -14 z^5 a^{-7} +z^5 a^{-9} +14 a^2 z^4+43 z^4 a^{-2} +28 z^4 a^{-4} +4 z^4 a^{-6} -4 z^4 a^{-8} +37 z^4+5 a^3 z^3+10 a z^3+9 z^3 a^{-1} +13 z^3 a^{-3} +13 z^3 a^{-5} +4 z^3 a^{-7} -8 a^2 z^2-23 z^2 a^{-2} -7 z^2 a^{-4} +z^2 a^{-6} -23 z^2-2 a^3 z-5 a z-7 z a^{-1} -7 z a^{-3} -3 z a^{-5} +2 a^2+6 a^{-2} +2 a^{-4} +7 }[/math] |
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