K12a121
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-7 q^3+13 q^2-17 q+21-22 q^{-1} +20 q^{-2} -16 q^{-3} +11 q^{-4} -6 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-33 t+45-33 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4+z^2+1 }[/math] |
| Determinant | 141 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+2 z^4 a^4+4 z^2 a^4+3 a^4-z^6 a^2-2 z^4 a^2-4 z^2 a^2-3 a^2-z^6-z^4+1+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}+3 a^4 z^{10}+6 a^2 z^{10}+3 z^{10}+4 a^5 z^9+6 a^3 z^9+7 a z^9+5 z^9 a^{-1} +3 a^6 z^8-4 a^4 z^8-10 a^2 z^8+6 z^8 a^{-2} +3 z^8+a^7 z^7-13 a^5 z^7-25 a^3 z^7-18 a z^7-2 z^7 a^{-1} +5 z^7 a^{-3} -12 a^6 z^6-12 a^4 z^6-3 a^2 z^6-6 z^6 a^{-2} +3 z^6 a^{-4} -12 z^6-4 a^7 z^5+10 a^5 z^5+29 a^3 z^5+18 a z^5-4 z^5 a^{-1} -6 z^5 a^{-3} +z^5 a^{-5} +14 a^6 z^4+24 a^4 z^4+17 a^2 z^4-5 z^4 a^{-4} +12 z^4+4 a^7 z^3-a^5 z^3-16 a^3 z^3-12 a z^3+2 z^3 a^{-1} +z^3 a^{-3} -2 z^3 a^{-5} -6 a^6 z^2-15 a^4 z^2-15 a^2 z^2+3 z^2 a^{-2} +3 z^2 a^{-4} -6 z^2-a^7 z+4 a^3 z+4 a z+z a^{-1} +z a^{-3} +z a^{-5} +a^6+3 a^4+3 a^2-2 a^{-2} - a^{-4} +1 }[/math] |
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