K12a257
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-16 q^6+23 q^5-28 q^4+30 q^3-28 q^2+23 q-15+9 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-16 t^2+46 t-63+46 t^{-1} -16 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-4 z^4+1 }[/math] |
| Determinant | 191 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} -2 z^4 a^{-6} -2 z^4+a^2 z^2-z^2 a^{-6} +z^2 a^{-8} -z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +4 z^{10} a^{-2} +8 z^{10} a^{-4} +4 z^{10} a^{-6} +7 z^9 a^{-1} +15 z^9 a^{-3} +15 z^9 a^{-5} +7 z^9 a^{-7} +7 z^8 a^{-2} +z^8 a^{-4} +8 z^8 a^{-6} +7 z^8 a^{-8} +7 z^8+4 a z^7-9 z^7 a^{-1} -32 z^7 a^{-3} -30 z^7 a^{-5} -7 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-28 z^6 a^{-2} -27 z^6 a^{-4} -30 z^6 a^{-6} -14 z^6 a^{-8} +z^6 a^{-10} -15 z^6-9 a z^5+24 z^5 a^{-3} +17 z^5 a^{-5} -7 z^5 a^{-7} -9 z^5 a^{-9} -2 a^2 z^4+25 z^4 a^{-2} +27 z^4 a^{-4} +24 z^4 a^{-6} +8 z^4 a^{-8} -2 z^4 a^{-10} +10 z^4+5 a z^3-9 z^3 a^{-3} -2 z^3 a^{-5} +8 z^3 a^{-7} +6 z^3 a^{-9} +a^2 z^2-8 z^2 a^{-2} -7 z^2 a^{-4} -6 z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} -3 z^2+z a^{-1} +2 z a^{-3} -2 z a^{-7} -z a^{-9} +1 }[/math] |
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