K12a968
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+8 q^4-15 q^3+22 q^2-28 q+31-29 q^{-1} +24 q^{-2} -17 q^{-3} +10 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+23 t^2-40 t+49-40 t^{-1} +23 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-5 z^4-4 z^2+1 }[/math] |
| Determinant | 193 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-6 a^2 z^4-7 z^4 a^{-2} +z^4 a^{-4} +6 z^4+2 a^4 z^2-5 a^2 z^2-8 z^2 a^{-2} +3 z^2 a^{-4} +4 z^2+a^4-a^2-3 a^{-2} +2 a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+6 z^{10} a^{-2} +12 z^{10}+9 a^3 z^9+13 a z^9+12 z^9 a^{-1} +8 z^9 a^{-3} +8 a^4 z^8-7 z^8 a^{-2} +6 z^8 a^{-4} -21 z^8+4 a^5 z^7-15 a^3 z^7-38 a z^7-43 z^7 a^{-1} -21 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-17 a^4 z^6-23 a^2 z^6-7 z^6 a^{-2} -15 z^6 a^{-4} +z^6 a^{-6} +4 z^6-8 a^5 z^5+3 a^3 z^5+34 a z^5+57 z^5 a^{-1} +27 z^5 a^{-3} -7 z^5 a^{-5} -2 a^6 z^4+11 a^4 z^4+25 a^2 z^4+24 z^4 a^{-2} +14 z^4 a^{-4} -3 z^4 a^{-6} +19 z^4+4 a^5 z^3+a^3 z^3-9 a z^3-29 z^3 a^{-1} -20 z^3 a^{-3} +3 z^3 a^{-5} +a^6 z^2-6 a^4 z^2-10 a^2 z^2-18 z^2 a^{-2} -9 z^2 a^{-4} +2 z^2 a^{-6} -10 z^2-a^5 z-a^3 z+a z+5 z a^{-1} +4 z a^{-3} +a^4+a^2+3 a^{-2} +2 a^{-4} +2 }[/math] |
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