K12a605
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-4 q^4+8 q^3-13 q^2+19 q-22+24 q^{-1} -22 q^{-2} +18 q^{-3} -13 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-20 t^2+30 t-33+30 t^{-1} -20 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-6 z^4-z^2+1 }[/math] |
| Determinant | 155 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-5 a^2 z^6+z^6 a^{-2} -4 z^6+4 a^4 z^4-10 a^2 z^4+3 z^4 a^{-2} -3 z^4+5 a^4 z^2-11 a^2 z^2+z^2 a^{-2} +4 z^2+2 a^4-5 a^2- a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+5 z^{10} a^{-2} +11 z^{10}+10 a^3 z^9+10 a z^9+4 z^9 a^{-1} +4 z^9 a^{-3} +12 a^4 z^8-a^2 z^8-19 z^8 a^{-2} +z^8 a^{-4} -33 z^8+10 a^5 z^7-14 a^3 z^7-44 a z^7-38 z^7 a^{-1} -18 z^7 a^{-3} +6 a^6 z^6-23 a^4 z^6-34 a^2 z^6+18 z^6 a^{-2} -4 z^6 a^{-4} +17 z^6+3 a^7 z^5-16 a^5 z^5-10 a^3 z^5+35 a z^5+51 z^5 a^{-1} +25 z^5 a^{-3} +a^8 z^4-5 a^6 z^4+18 a^4 z^4+41 a^2 z^4+z^4 a^{-2} +5 z^4 a^{-4} +13 z^4-2 a^7 z^3+14 a^5 z^3+20 a^3 z^3-3 a z^3-17 z^3 a^{-1} -10 z^3 a^{-3} -a^8 z^2+2 a^6 z^2-7 a^4 z^2-22 a^2 z^2-4 z^2 a^{-2} -2 z^2 a^{-4} -14 z^2-4 a^5 z-8 a^3 z-5 a z-z a^{-1} +2 a^4+5 a^2+ a^{-2} +5 }[/math] |
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