K12a704
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-10 q^2+18 q-25+31 q^{-1} -32 q^{-2} +30 q^{-3} -24 q^{-4} +16 q^{-5} -8 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-24 t^2+43 t-51+43 t^{-1} -24 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+4 z^4+3 z^2+1 }[/math] |
| Determinant | 203 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+7 a^4 z^4-7 a^2 z^4-z^4 a^{-2} +6 z^4-3 a^6 z^2+9 a^4 z^2-7 a^2 z^2-2 z^2 a^{-2} +6 z^2-2 a^6+4 a^4-3 a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+7 a^4 z^{10}+13 a^2 z^{10}+6 z^{10}+11 a^5 z^9+19 a^3 z^9+15 a z^9+7 z^9 a^{-1} +10 a^6 z^8+3 a^4 z^8-16 a^2 z^8+4 z^8 a^{-2} -5 z^8+6 a^7 z^7-18 a^5 z^7-56 a^3 z^7-51 a z^7-18 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-18 a^6 z^6-37 a^4 z^6-26 a^2 z^6-12 z^6 a^{-2} -22 z^6+a^9 z^5-7 a^7 z^5+14 a^5 z^5+49 a^3 z^5+41 a z^5+11 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+21 a^6 z^4+52 a^4 z^4+44 a^2 z^4+12 z^4 a^{-2} +29 z^4-2 a^9 z^3+3 a^7 z^3-15 a^3 z^3-13 a z^3+3 z^3 a^{-3} +a^8 z^2-11 a^6 z^2-25 a^4 z^2-22 a^2 z^2-5 z^2 a^{-2} -14 z^2+a^9 z-a^7 z-2 a^5 z+a^3 z+a z-z a^{-1} -z a^{-3} +2 a^6+4 a^4+3 a^2+ a^{-2} +3 }[/math] |
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