K12a808
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-4 q^3+8 q^2-12 q+17-20 q^{-1} +21 q^{-2} -19 q^{-3} +16 q^{-4} -11 q^{-5} +7 q^{-6} -4 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+15 t^2-32 t+41-32 t^{-1} +15 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-3 z^4+z^2+1 }[/math] |
| Determinant | 141 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^6+z^2 a^6-a^6-z^6 a^4-2 z^4 a^4+2 a^4-z^6 a^2-z^4 a^2-a^2-z^6-2 z^4-z^2+1+z^4 a^{-2} +z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^5 z^{11}+3 a^3 z^{11}+6 a^6 z^{10}+14 a^4 z^{10}+8 a^2 z^{10}+4 a^7 z^9-4 a^5 z^9+2 a^3 z^9+10 a z^9+a^8 z^8-29 a^6 z^8-63 a^4 z^8-23 a^2 z^8+10 z^8-19 a^7 z^7-28 a^5 z^7-41 a^3 z^7-22 a z^7+10 z^7 a^{-1} -4 a^8 z^6+42 a^6 z^6+88 a^4 z^6+22 a^2 z^6+8 z^6 a^{-2} -12 z^6+25 a^7 z^5+58 a^5 z^5+63 a^3 z^5+15 a z^5-11 z^5 a^{-1} +4 z^5 a^{-3} +3 a^8 z^4-22 a^6 z^4-44 a^4 z^4-13 a^2 z^4-8 z^4 a^{-2} +z^4 a^{-4} -3 z^4-10 a^7 z^3-30 a^5 z^3-31 a^3 z^3-8 a z^3+z^3 a^{-1} -2 z^3 a^{-3} +2 a^6 z^2+4 a^4 z^2+2 a^2 z^2+2 z^2 a^{-2} +2 z^2+3 a^5 z+5 a^3 z+2 a z+a^6+2 a^4+a^2+1 }[/math] |
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