K12a60
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-22 q^3+33 q^2-39 q+42-39 q^{-1} +31 q^{-2} -21 q^{-3} +11 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+28 t^2-57 t+73-57 t^{-1} +28 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^2+1 }[/math] |
| Determinant | 261 |
| 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^2-9 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +10 z^2+2 a^4-5 a^2- a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +8 a^2 z^{10}+8 z^{10} a^{-2} +16 z^{10}+12 a^3 z^9+30 a z^9+31 z^9 a^{-1} +13 z^9 a^{-3} +9 a^4 z^8+9 a^2 z^8+15 z^8 a^{-2} +11 z^8 a^{-4} +4 z^8+4 a^5 z^7-19 a^3 z^7-70 a z^7-67 z^7 a^{-1} -15 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-17 a^4 z^6-50 a^2 z^6-63 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} -74 z^6-7 a^5 z^5+12 a^3 z^5+53 a z^5+38 z^5 a^{-1} -4 z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+15 a^4 z^4+58 a^2 z^4+57 z^4 a^{-2} +14 z^4 a^{-4} -z^4 a^{-6} +83 z^4+4 a^5 z^3-4 a^3 z^3-19 a z^3-8 z^3 a^{-1} +7 z^3 a^{-3} +4 z^3 a^{-5} +a^6 z^2-8 a^4 z^2-29 a^2 z^2-20 z^2 a^{-2} -4 z^2 a^{-4} -36 z^2-a^5 z+a^3 z+4 a z+2 z a^{-1} +2 a^4+5 a^2+ a^{-2} +5 }[/math] |
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