K12a261
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-12 q^3+21 q^2-30 q+37-38 q^{-1} +35 q^{-2} -28 q^{-3} +19 q^{-4} -10 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+27 t^2-52 t+65-52 t^{-1} +27 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^4+1 }[/math] |
| Determinant | 241 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +4 z^6+3 a^4 z^4-9 a^2 z^4-2 z^4 a^{-2} +7 z^4-a^6 z^2+6 a^4 z^2-9 a^2 z^2-z^2 a^{-2} +5 z^2-a^6+3 a^4-3 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+15 a^2 z^{10}+9 z^{10}+7 a^5 z^9+20 a^3 z^9+30 a z^9+17 z^9 a^{-1} +4 a^6 z^8-a^4 z^8-8 a^2 z^8+18 z^8 a^{-2} +15 z^8+a^7 z^7-17 a^5 z^7-61 a^3 z^7-72 a z^7-17 z^7 a^{-1} +12 z^7 a^{-3} -12 a^6 z^6-32 a^4 z^6-53 a^2 z^6-25 z^6 a^{-2} +5 z^6 a^{-4} -63 z^6-3 a^7 z^5+11 a^5 z^5+49 a^3 z^5+45 a z^5-4 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} +13 a^6 z^4+43 a^4 z^4+66 a^2 z^4+13 z^4 a^{-2} -3 z^4 a^{-4} +52 z^4+3 a^7 z^3-13 a^3 z^3-9 a z^3+5 z^3 a^{-1} +4 z^3 a^{-3} -6 a^6 z^2-20 a^4 z^2-26 a^2 z^2-3 z^2 a^{-2} -15 z^2-a^7 z-a^5 z+a^3 z+a z+a^6+3 a^4+3 a^2+2 }[/math] |
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