K12a33
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-10 q^3+18 q^2-24 q+29-30 q^{-1} +27 q^{-2} -21 q^{-3} +14 q^{-4} -7 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+22 t^2-40 t+49-40 t^{-1} +22 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +5 z^6+3 a^4 z^4-12 a^2 z^4-3 z^4 a^{-2} +12 z^4-a^6 z^2+9 a^4 z^2-18 a^2 z^2-4 z^2 a^{-2} +15 z^2-2 a^6+7 a^4-10 a^2-2 a^{-2} +8 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+8 a^2 z^{10}+5 z^{10}+4 a^5 z^9+12 a^3 z^9+19 a z^9+11 z^9 a^{-1} +3 a^6 z^8+3 a^4 z^8+2 a^2 z^8+13 z^8 a^{-2} +15 z^8+a^7 z^7-9 a^5 z^7-34 a^3 z^7-42 a z^7-9 z^7 a^{-1} +9 z^7 a^{-3} -11 a^6 z^6-31 a^4 z^6-51 a^2 z^6-21 z^6 a^{-2} +4 z^6 a^{-4} -56 z^6-4 a^7 z^5+a^5 z^5+24 a^3 z^5+23 a z^5-9 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +14 a^6 z^4+46 a^4 z^4+74 a^2 z^4+17 z^4 a^{-2} -4 z^4 a^{-4} +63 z^4+5 a^7 z^3+7 a^5 z^3-3 a^3 z^3+13 z^3 a^{-1} +7 z^3 a^{-3} -z^3 a^{-5} -8 a^6 z^2-29 a^4 z^2-46 a^2 z^2-9 z^2 a^{-2} +z^2 a^{-4} -35 z^2-2 a^7 z-3 a^5 z-a^3 z-2 a z-4 z a^{-1} -2 z a^{-3} +2 a^6+7 a^4+10 a^2+2 a^{-2} +8 }[/math] |
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