K12a273
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-17 q^3+25 q^2-30 q+33-30 q^{-1} +25 q^{-2} -17 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+21 t^2-47 t+61-47 t^{-1} +21 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-3 z^4+z^2+1 }[/math] |
| Determinant | 205 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-a^2 z^4-z^4 a^{-2} +z^4 a^{-4} -3 z^4+a^4 z^2-a^2 z^2-z^2 a^{-2} +z^2 a^{-4} +z^2-a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+6 z^{10} a^{-2} +12 z^{10}+8 a^3 z^9+13 a z^9+13 z^9 a^{-1} +8 z^9 a^{-3} +7 a^4 z^8-a^2 z^8-z^8 a^{-2} +7 z^8 a^{-4} -16 z^8+4 a^5 z^7-10 a^3 z^7-30 a z^7-30 z^7 a^{-1} -10 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-13 a^4 z^6-13 a^2 z^6-13 z^6 a^{-2} -13 z^6 a^{-4} +z^6 a^{-6} +2 z^6-9 a^5 z^5-4 a^3 z^5+17 a z^5+17 z^5 a^{-1} -4 z^5 a^{-3} -9 z^5 a^{-5} -2 a^6 z^4+6 a^4 z^4+11 a^2 z^4+11 z^4 a^{-2} +6 z^4 a^{-4} -2 z^4 a^{-6} +6 z^4+6 a^5 z^3+9 a^3 z^3+5 a z^3+5 z^3 a^{-1} +9 z^3 a^{-3} +6 z^3 a^{-5} +a^6 z^2-a^4 z^2-4 a^2 z^2-4 z^2 a^{-2} -z^2 a^{-4} +z^2 a^{-6} -4 z^2-a^5 z-4 a^3 z-6 a z-6 z a^{-1} -4 z a^{-3} -z a^{-5} +a^2+ a^{-2} +3 }[/math] |
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