K12a77
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+11 q^4-19 q^3+28 q^2-33 q+36-33 q^{-1} +26 q^{-2} -18 q^{-3} +10 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+24 t^2-49 t+63-49 t^{-1} +24 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+2 z^4+1 }[/math] |
| Determinant | 225 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +5 z^6+a^4 z^4-7 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +13 z^4+2 a^4 z^2-11 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} +15 z^2+2 a^4-6 a^2-2 a^{-2} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +5 a^2 z^{10}+5 z^{10} a^{-2} +10 z^{10}+9 a^3 z^9+24 a z^9+25 z^9 a^{-1} +10 z^9 a^{-3} +8 a^4 z^8+13 a^2 z^8+19 z^8 a^{-2} +10 z^8 a^{-4} +14 z^8+4 a^5 z^7-12 a^3 z^7-53 a z^7-51 z^7 a^{-1} -9 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-16 a^4 z^6-51 a^2 z^6-68 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} -81 z^6-8 a^5 z^5+2 a^3 z^5+39 a z^5+25 z^5 a^{-1} -13 z^5 a^{-3} -9 z^5 a^{-5} -2 a^6 z^4+12 a^4 z^4+57 a^2 z^4+66 z^4 a^{-2} +13 z^4 a^{-4} -z^4 a^{-6} +95 z^4+5 a^5 z^3+a^3 z^3-12 a z^3+z^3 a^{-1} +13 z^3 a^{-3} +4 z^3 a^{-5} +a^6 z^2-6 a^4 z^2-30 a^2 z^2-25 z^2 a^{-2} -4 z^2 a^{-4} -44 z^2-a^5 z+2 a z-z a^{-3} +2 a^4+6 a^2+2 a^{-2} +7 }[/math] |
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