K12a744
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+3 q^2-4 q+6-7 q^{-1} +8 q^{-2} -8 q^{-3} +7 q^{-4} -6 q^{-5} +5 q^{-6} -3 q^{-7} +2 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^2-15 t+23-15 t^{-1} +4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^4+z^2+1 }[/math] |
| Determinant | 61 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^8-a^8+z^4 a^6+2 z^2 a^6+2 a^6+z^4 a^4-a^4+z^4 a^2+z^4+z^2+1-z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^7 z^{11}+a^5 z^{11}+2 a^8 z^{10}+5 a^6 z^{10}+3 a^4 z^{10}+a^9 z^9-3 a^7 z^9+4 a^3 z^9-14 a^8 z^8-31 a^6 z^8-13 a^4 z^8+4 a^2 z^8-7 a^9 z^7-9 a^7 z^7-21 a^5 z^7-15 a^3 z^7+4 a z^7+33 a^8 z^6+63 a^6 z^6+16 a^4 z^6-10 a^2 z^6+4 z^6+16 a^9 z^5+36 a^7 z^5+45 a^5 z^5+15 a^3 z^5-6 a z^5+4 z^5 a^{-1} -32 a^8 z^4-53 a^6 z^4-11 a^4 z^4+4 a^2 z^4+3 z^4 a^{-2} -3 z^4-14 a^9 z^3-33 a^7 z^3-29 a^5 z^3-6 a^3 z^3-3 z^3 a^{-1} +z^3 a^{-3} +12 a^8 z^2+19 a^6 z^2+7 a^4 z^2-2 z^2 a^{-2} -2 z^2+4 a^9 z+8 a^7 z+5 a^5 z+a^3 z-a^8-2 a^6-a^4+1 }[/math] |
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