K12a1260
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-13 q^3+18 q^2-22 q+25-22 q^{-1} +18 q^{-2} -13 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+4 t^4-10 t^3+19 t^2-27 t+31-27 t^{-1} +19 t^{-2} -10 t^{-3} +4 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-6 z^8-13 z^6-11 z^4-2 z^2+1 }[/math] |
| Determinant | 153 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -8 z^8+6 a^2 z^6+6 z^6 a^{-2} -25 z^6+13 a^2 z^4+13 z^4 a^{-2} -37 z^4+11 a^2 z^2+11 z^2 a^{-2} -24 z^2+2 a^2+2 a^{-2} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+5 z^{10} a^{-2} +10 z^{10}+6 a^3 z^9+3 a z^9+3 z^9 a^{-1} +6 z^9 a^{-3} +5 a^4 z^8-12 a^2 z^8-12 z^8 a^{-2} +5 z^8 a^{-4} -34 z^8+3 a^5 z^7-15 a^3 z^7-19 a z^7-19 z^7 a^{-1} -15 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-12 a^4 z^6+17 a^2 z^6+17 z^6 a^{-2} -12 z^6 a^{-4} +z^6 a^{-6} +60 z^6-8 a^5 z^5+15 a^3 z^5+34 a z^5+34 z^5 a^{-1} +15 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+7 a^4 z^4-17 a^2 z^4-17 z^4 a^{-2} +7 z^4 a^{-4} -3 z^4 a^{-6} -54 z^4+5 a^5 z^3-9 a^3 z^3-21 a z^3-21 z^3 a^{-1} -9 z^3 a^{-3} +5 z^3 a^{-5} +2 a^6 z^2-2 a^4 z^2+10 a^2 z^2+10 z^2 a^{-2} -2 z^2 a^{-4} +2 z^2 a^{-6} +28 z^2-a^5 z+3 a z+3 z a^{-1} -z a^{-5} -2 a^2-2 a^{-2} -3 }[/math] |
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