K12a1200
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-4 q^4+9 q^3-15 q^2+23 q-28+30 q^{-1} -29 q^{-2} +24 q^{-3} -17 q^{-4} +10 q^{-5} -4 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-25 t^2+39 t-43+39 t^{-1} -25 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-5 z^4-3 z^2+1 }[/math] |
| Determinant | 195 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-4 a^2 z^6+z^6 a^{-2} -4 z^6+3 a^4 z^4-6 a^2 z^4+3 z^4 a^{-2} -5 z^4+3 a^4 z^2-6 a^2 z^2+2 z^2 a^{-2} -2 z^2+2 a^4-3 a^2+ a^{-2} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +10 a^2 z^{10}+6 z^{10} a^{-2} +16 z^{10}+18 a^3 z^9+16 a z^9+2 z^9 a^{-1} +4 z^9 a^{-3} +21 a^4 z^8-4 a^2 z^8-23 z^8 a^{-2} +z^8 a^{-4} -49 z^8+17 a^5 z^7-31 a^3 z^7-69 a z^7-38 z^7 a^{-1} -17 z^7 a^{-3} +10 a^6 z^6-37 a^4 z^6-42 a^2 z^6+26 z^6 a^{-2} -4 z^6 a^{-4} +35 z^6+4 a^7 z^5-22 a^5 z^5+8 a^3 z^5+66 a z^5+55 z^5 a^{-1} +23 z^5 a^{-3} +a^8 z^4-7 a^6 z^4+21 a^4 z^4+44 a^2 z^4-7 z^4 a^{-2} +5 z^4 a^{-4} +3 z^4+10 a^5 z^3-3 a^3 z^3-25 a z^3-22 z^3 a^{-1} -10 z^3 a^{-3} +3 a^6 z^2-8 a^4 z^2-19 a^2 z^2-2 z^2 a^{-4} -6 z^2-a^5 z+2 a^3 z+5 a z+3 z a^{-1} +z a^{-3} +2 a^4+3 a^2- a^{-2} +1 }[/math] |
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