K12a259
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-3 q^6+6 q^5-10 q^4+14 q^3-16 q^2+17 q-16+13 q^{-1} -9 q^{-2} +6 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-12 t^2+27 t-33+27 t^{-1} -12 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-3 z^2+1 }[/math] |
| Determinant | 115 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-2 a^2 z^4+2 z^4 a^{-2} -2 z^4 a^{-4} +2 z^4+a^4 z^2-4 a^2 z^2+2 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-6} +z^2+a^4-a^2+2 a^{-2} -2 a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+3 z^{10} a^{-2} +6 z^{10}+3 a^3 z^9+4 a z^9+6 z^9 a^{-1} +5 z^9 a^{-3} +a^4 z^8-11 a^2 z^8+6 z^8 a^{-4} -18 z^8-15 a^3 z^7-31 a z^7-27 z^7 a^{-1} -5 z^7 a^{-3} +6 z^7 a^{-5} -5 a^4 z^6+5 a^2 z^6-14 z^6 a^{-2} -5 z^6 a^{-4} +5 z^6 a^{-6} +6 z^6+23 a^3 z^5+46 a z^5+27 z^5 a^{-1} -4 z^5 a^{-3} -5 z^5 a^{-5} +3 z^5 a^{-7} +8 a^4 z^4+13 a^2 z^4+8 z^4 a^{-2} -5 z^4 a^{-4} -5 z^4 a^{-6} +z^4 a^{-8} +12 z^4-12 a^3 z^3-22 a z^3-12 z^3 a^{-1} +z^3 a^{-3} -3 z^3 a^{-7} -5 a^4 z^2-10 a^2 z^2+2 z^2 a^{-2} +7 z^2 a^{-4} +3 z^2 a^{-6} -z^2 a^{-8} -6 z^2+2 a^3 z+3 a z+2 z a^{-1} +z a^{-3} +z a^{-5} +z a^{-7} +a^4+a^2-2 a^{-2} -2 a^{-4} - a^{-6} }[/math] |
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