K12a425
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+2 q^4-4 q^3+7 q^2-9 q+12-12 q^{-1} +11 q^{-2} -9 q^{-3} +7 q^{-4} -4 q^{-5} +2 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 6 t^2-20 t+29-20 t^{-1} +6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 6 z^4+4 z^2+1 }[/math] |
| Determinant | 81 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+z^4 a^4+z^2 a^4+a^4+2 z^4 a^2+2 z^2 a^2+2 z^4+2 z^2+1+z^4 a^{-2} +z^2 a^{-2} + a^{-2} -z^2 a^{-4} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+2 a^4 z^{10}+4 a^2 z^{10}+2 z^{10}+2 a^5 z^9-2 a^3 z^9-2 a z^9+2 z^9 a^{-1} +2 a^6 z^8-7 a^4 z^8-18 a^2 z^8+2 z^8 a^{-2} -7 z^8+a^7 z^7-6 a^5 z^7-a^3 z^7-4 z^7 a^{-1} +2 z^7 a^{-3} -9 a^6 z^6+6 a^4 z^6+32 a^2 z^6-2 z^6 a^{-2} +2 z^6 a^{-4} +13 z^6-5 a^7 z^5-a^5 z^5+2 a^3 z^5+6 a z^5+5 z^5 a^{-1} -2 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4-2 a^4 z^4-24 a^2 z^4-z^4 a^{-2} -5 z^4 a^{-4} -7 z^4+7 a^7 z^3+8 a^5 z^3-2 a^3 z^3-4 a z^3-z^3 a^{-1} -3 z^3 a^{-3} -3 z^3 a^{-5} -5 a^6 z^2-2 a^4 z^2+5 a^2 z^2+2 z^2 a^{-2} +3 z^2 a^{-4} +z^2-3 a^7 z-3 a^5 z+a^3 z+a z+2 z a^{-3} +2 z a^{-5} +a^6+a^4- a^{-2} - a^{-4} +1 }[/math] |
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