K12a454
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-3 q^6+6 q^5-9 q^4+13 q^3-15 q^2+15 q-14+11 q^{-1} -8 q^{-2} +5 q^{-3} -2 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-12 t^2+24 t-27+24 t^{-1} -12 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-6 z^2+1 }[/math] |
| Determinant | 103 |
| 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+z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-6} +2 a^4-2 a^2+ a^{-2} - a^{-4} + a^{-6} }[/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+3 z^9 a^{-1} +5 z^9 a^{-3} +a^4 z^8-7 a^2 z^8-4 z^8 a^{-2} +6 z^8 a^{-4} -18 z^8-10 a^3 z^7-11 a z^7-16 z^7 a^{-1} -9 z^7 a^{-3} +6 z^7 a^{-5} -6 a^4 z^6+2 a^2 z^6-2 z^6 a^{-2} -9 z^6 a^{-4} +5 z^6 a^{-6} +20 z^6+15 a^3 z^5+13 a z^5+13 z^5 a^{-1} +4 z^5 a^{-3} -8 z^5 a^{-5} +3 z^5 a^{-7} +12 a^4 z^4+10 a^2 z^4-2 z^4 a^{-2} +3 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} -14 z^4-7 a^3 z^3-a z^3-2 z^3 a^{-1} +5 z^3 a^{-5} -3 z^3 a^{-7} -9 a^4 z^2-8 a^2 z^2+4 z^2 a^{-2} +3 z^2 a^{-4} +3 z^2 a^{-6} -z^2 a^{-8} +6 z^2+a^3 z-2 a z-2 z a^{-1} -z a^{-5} +2 a^4+2 a^2- a^{-2} - a^{-4} - a^{-6} }[/math] |
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