K12a463
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-3 q^6+6 q^5-10 q^4+14 q^3-16 q^2+17 q-15+12 q^{-1} -9 q^{-2} +5 q^{-3} -2 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-12 t^2+26 t-31+26 t^{-1} -12 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-4 z^2+1 }[/math] |
| Determinant | 111 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-2 a^2 z^4+2 z^4 a^{-2} -2 z^4 a^{-4} +2 z^4+a^4 z^2-5 a^2 z^2+2 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-6} +z^2+2 a^4-3 a^2+2 a^{-2} -2 a^{-4} + a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+3 z^{10} a^{-2} +5 z^{10}+2 a^3 z^9+a z^9+4 z^9 a^{-1} +5 z^9 a^{-3} +a^4 z^8-6 a^2 z^8-z^8 a^{-2} +6 z^8 a^{-4} -14 z^8-10 a^3 z^7-15 a z^7-16 z^7 a^{-1} -5 z^7 a^{-3} +6 z^7 a^{-5} -6 a^4 z^6-3 a^2 z^6-10 z^6 a^{-2} -5 z^6 a^{-4} +5 z^6 a^{-6} +3 z^6+16 a^3 z^5+20 a z^5+7 z^5 a^{-1} -5 z^5 a^{-3} -5 z^5 a^{-5} +3 z^5 a^{-7} +12 a^4 z^4+20 a^2 z^4+4 z^4 a^{-2} -5 z^4 a^{-4} -5 z^4 a^{-6} +z^4 a^{-8} +11 z^4-10 a^3 z^3-9 a z^3+2 z^3 a^{-1} +4 z^3 a^{-3} -3 z^3 a^{-7} -9 a^4 z^2-16 a^2 z^2+3 z^2 a^{-2} +7 z^2 a^{-4} +3 z^2 a^{-6} -z^2 a^{-8} -7 z^2+3 a^3 z+3 a z+z a^{-5} +z a^{-7} +2 a^4+3 a^2-2 a^{-2} -2 a^{-4} - a^{-6} +1 }[/math] |
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