K12a1279
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-2 q^4+4 q^3-5 q^2+7 q-9+9 q^{-1} -9 q^{-2} +8 q^{-3} -6 q^{-4} +4 q^{-5} -2 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -6 t^2+17 t-21+17 t^{-1} -6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -6 z^4-7 z^2+1 }[/math] |
| Determinant | 67 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^6+a^6-z^4 a^4-z^2 a^4-2 z^4 a^2-3 z^2 a^2-2 z^4-4 z^2-2-z^4 a^{-2} -z^2 a^{-2} + a^{-2} +z^2 a^{-4} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+2 z^{10} a^{-2} +4 z^{10}+3 a^3 z^9-2 a z^9-3 z^9 a^{-1} +2 z^9 a^{-3} +3 a^4 z^8-7 a^2 z^8-10 z^8 a^{-2} +z^8 a^{-4} -21 z^8+3 a^5 z^7-12 a^3 z^7-5 a z^7-z^7 a^{-1} -11 z^7 a^{-3} +3 a^6 z^6-8 a^4 z^6+8 a^2 z^6+14 z^6 a^{-2} -6 z^6 a^{-4} +39 z^6+2 a^7 z^5-6 a^5 z^5+23 a^3 z^5+17 a z^5+3 z^5 a^{-1} +17 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+10 a^4 z^4-a^2 z^4-8 z^4 a^{-2} +11 z^4 a^{-4} -37 z^4-3 a^7 z^3+6 a^5 z^3-20 a^3 z^3-20 a z^3+2 z^3 a^{-1} -7 z^3 a^{-3} -2 a^8 z^2+5 a^6 z^2-2 a^4 z^2-5 a^2 z^2+5 z^2 a^{-2} -7 z^2 a^{-4} +16 z^2+6 a^3 z+5 a z-z a^{-1} -a^6- a^{-2} + a^{-4} -2 }[/math] |
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