K12a179
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-7 q^6+12 q^5-16 q^4+20 q^3-21 q^2+19 q-15+11 q^{-1} -6 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-18 t^2+27 t-29+27 t^{-1} -18 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+4 z^4+2 z^2+1 }[/math] |
| Determinant | 135 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-10 z^4 a^{-2} +8 z^4 a^{-4} -z^4 a^{-6} +8 z^4-3 a^2 z^2-11 z^2 a^{-2} +10 z^2 a^{-4} -3 z^2 a^{-6} +9 z^2-a^2-5 a^{-2} +5 a^{-4} -2 a^{-6} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +6 z^{10} a^{-2} +3 z^{10} a^{-4} +3 z^{10}+4 a z^9+6 z^9 a^{-1} +7 z^9 a^{-3} +5 z^9 a^{-5} +3 a^2 z^8-11 z^8 a^{-2} +2 z^8 a^{-4} +6 z^8 a^{-6} -4 z^8+a^3 z^7-13 a z^7-27 z^7 a^{-1} -23 z^7 a^{-3} -5 z^7 a^{-5} +5 z^7 a^{-7} -12 a^2 z^6-6 z^6 a^{-2} -16 z^6 a^{-4} -9 z^6 a^{-6} +3 z^6 a^{-8} -14 z^6-4 a^3 z^5+9 a z^5+30 z^5 a^{-1} +27 z^5 a^{-3} +2 z^5 a^{-5} -7 z^5 a^{-7} +z^5 a^{-9} +14 a^2 z^4+27 z^4 a^{-2} +27 z^4 a^{-4} +8 z^4 a^{-6} -5 z^4 a^{-8} +27 z^4+4 a^3 z^3-12 z^3 a^{-1} -13 z^3 a^{-3} -z^3 a^{-5} +2 z^3 a^{-7} -2 z^3 a^{-9} -7 a^2 z^2-21 z^2 a^{-2} -20 z^2 a^{-4} -7 z^2 a^{-6} +2 z^2 a^{-8} -17 z^2-a^3 z-a z+2 z a^{-1} +3 z a^{-3} +z a^{-9} +a^2+5 a^{-2} +5 a^{-4} +2 a^{-6} +4 }[/math] |
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