K12a945
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-10 q^6+17 q^5-24 q^4+30 q^3-31 q^2+29 q-23+16 q^{-1} -9 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-20 t^2+46 t-59+46 t^{-1} -20 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+4 z^4+2 z^2+1 }[/math] |
| Determinant | 199 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+4 z^4 a^{-2} +z^4 a^{-4} -z^4 a^{-6} +z^4-a^2 z^2+3 z^2 a^{-2} +z^2 a^{-4} -z^2 a^{-6} + a^{-2} + a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +13 z^{10} a^{-2} +7 z^{10} a^{-4} +6 z^{10}+7 a z^9+12 z^9 a^{-1} +17 z^9 a^{-3} +12 z^9 a^{-5} +4 a^2 z^8-26 z^8 a^{-2} +2 z^8 a^{-4} +13 z^8 a^{-6} -11 z^8+a^3 z^7-22 a z^7-48 z^7 a^{-1} -51 z^7 a^{-3} -17 z^7 a^{-5} +9 z^7 a^{-7} -13 a^2 z^6+12 z^6 a^{-2} -25 z^6 a^{-4} -23 z^6 a^{-6} +4 z^6 a^{-8} -3 z^6-3 a^3 z^5+21 a z^5+54 z^5 a^{-1} +52 z^5 a^{-3} +8 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +12 a^2 z^4-2 z^4 a^{-2} +24 z^4 a^{-4} +19 z^4 a^{-6} -4 z^4 a^{-8} +9 z^4+2 a^3 z^3-8 a z^3-29 z^3 a^{-1} -27 z^3 a^{-3} +7 z^3 a^{-7} -z^3 a^{-9} -3 a^2 z^2+z^2 a^{-2} -7 z^2 a^{-4} -7 z^2 a^{-6} -2 z^2+2 a z+6 z a^{-1} +6 z a^{-3} -2 z a^{-7} - a^{-2} + a^{-4} + a^{-6} }[/math] |
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