K12a196
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-2 q^2+5 q-9+14 q^{-1} -18 q^{-2} +20 q^{-3} -19 q^{-4} +16 q^{-5} -12 q^{-6} +7 q^{-7} -3 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-13 t^2+30 t-37+30 t^{-1} -13 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-z^4-4 z^2+1 }[/math] |
| Determinant | 127 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-2 z^4 a^6-3 z^2 a^6-a^6+z^6 a^4+z^4 a^4-z^2 a^4-a^4+z^6 a^2+2 z^4 a^2+3 z^2 a^2+3 a^2-2 z^4-5 z^2-3+z^2 a^{-2} +2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+3 a^6 z^{10}+5 a^4 z^{10}+2 a^2 z^{10}+5 a^7 z^9+4 a^5 z^9+a^3 z^9+2 a z^9+5 a^8 z^8-2 a^6 z^8-12 a^4 z^8-3 a^2 z^8+2 z^8+3 a^9 z^7-11 a^7 z^7-12 a^5 z^7+2 z^7 a^{-1} +a^{10} z^6-13 a^8 z^6-6 a^6 z^6+20 a^4 z^6+10 a^2 z^6+z^6 a^{-2} -z^6-8 a^9 z^5+8 a^7 z^5+16 a^5 z^5-6 a z^5-6 z^5 a^{-1} -3 a^{10} z^4+10 a^8 z^4+10 a^6 z^4-16 a^4 z^4-18 a^2 z^4-4 z^4 a^{-2} -9 z^4+5 a^9 z^3-5 a^7 z^3-9 a^5 z^3+4 a z^3+5 z^3 a^{-1} +2 a^{10} z^2-5 a^8 z^2-6 a^6 z^2+7 a^4 z^2+12 a^2 z^2+5 z^2 a^{-2} +11 z^2-a^9 z+a^7 z+2 a^5 z-a z-z a^{-1} +a^8+a^6-a^4-3 a^2-2 a^{-2} -3 }[/math] |
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