K12a1199
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-15 q^3+22 q^2-27 q+29-27 q^{-1} +22 q^{-2} -15 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+5 t^4-13 t^3+23 t^2-32 t+37-32 t^{-1} +23 t^{-2} -13 t^{-3} +5 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-5 z^8-8 z^6-5 z^4-2 z^2+1 }[/math] |
| Determinant | 185 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -7 z^8+5 a^2 z^6+5 z^6 a^{-2} -18 z^6+8 a^2 z^4+8 z^4 a^{-2} -21 z^4+5 a^2 z^2+5 z^2 a^{-2} -12 z^2+2 a^2+2 a^{-2} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +8 a^2 z^{10}+7 z^{10} a^{-2} +15 z^{10}+10 a^3 z^9+6 a z^9+4 z^9 a^{-1} +8 z^9 a^{-3} +8 a^4 z^8-19 a^2 z^8-15 z^8 a^{-2} +7 z^8 a^{-4} -49 z^8+4 a^5 z^7-28 a^3 z^7-38 a z^7-26 z^7 a^{-1} -16 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-21 a^4 z^6+15 a^2 z^6+18 z^6 a^{-2} -15 z^6 a^{-4} +z^6 a^{-6} +71 z^6-9 a^5 z^5+27 a^3 z^5+59 a z^5+41 z^5 a^{-1} +9 z^5 a^{-3} -9 z^5 a^{-5} -2 a^6 z^4+14 a^4 z^4-2 a^2 z^4-18 z^4 a^{-2} +6 z^4 a^{-4} -2 z^4 a^{-6} -44 z^4+2 a^5 z^3-12 a^3 z^3-28 a z^3-24 z^3 a^{-1} -6 z^3 a^{-3} +4 z^3 a^{-5} -4 a^4 z^2+3 a^2 z^2+8 z^2 a^{-2} +z^2 a^{-6} +16 z^2+2 a^3 z+4 a z+4 z a^{-1} +2 z a^{-3} -2 a^2-2 a^{-2} -3 }[/math] |
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