K12a415
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+13 q^4-22 q^3+31 q^2-38 q+40-36 q^{-1} +29 q^{-2} -19 q^{-3} +10 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+27 t^2-54 t+69-54 t^{-1} +27 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^4-2 z^2+1 }[/math] |
| Determinant | 249 |
| 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^4-5 z^4 a^{-2} +z^4 a^{-4} +8 z^4+2 a^4 z^2-7 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +7 z^2+a^4-2 a^2-2 a^{-2} + a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +8 a^2 z^{10}+11 z^{10} a^{-2} +19 z^{10}+10 a^3 z^9+19 a z^9+25 z^9 a^{-1} +16 z^9 a^{-3} +8 a^4 z^8-a^2 z^8-7 z^8 a^{-2} +12 z^8 a^{-4} -28 z^8+4 a^5 z^7-14 a^3 z^7-52 a z^7-72 z^7 a^{-1} -33 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-15 a^4 z^6-21 a^2 z^6-21 z^6 a^{-2} -23 z^6 a^{-4} +z^6 a^{-6} -2 z^6-8 a^5 z^5+3 a^3 z^5+46 a z^5+65 z^5 a^{-1} +23 z^5 a^{-3} -7 z^5 a^{-5} -2 a^6 z^4+10 a^4 z^4+25 a^2 z^4+24 z^4 a^{-2} +12 z^4 a^{-4} -z^4 a^{-6} +24 z^4+5 a^5 z^3+2 a^3 z^3-15 a z^3-22 z^3 a^{-1} -9 z^3 a^{-3} +z^3 a^{-5} +a^6 z^2-4 a^4 z^2-13 a^2 z^2-10 z^2 a^{-2} -4 z^2 a^{-4} -14 z^2-a^5 z-a^3 z+a z+3 z a^{-1} +2 z a^{-3} +a^4+2 a^2+2 a^{-2} + a^{-4} +3 }[/math] |
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