K12a306
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-3 q^2+7 q-12+18 q^{-1} -21 q^{-2} +23 q^{-3} -22 q^{-4} +17 q^{-5} -12 q^{-6} +7 q^{-7} -3 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-14 t^2+35 t-45+35 t^{-1} -14 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^4-3 z^2+1 }[/math] |
| Determinant | 147 |
| 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-a^4+z^6 a^2+z^4 a^2+z^2 a^2+2 a^2-2 z^4-3 z^2-1+z^2 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+3 a^6 z^{10}+6 a^4 z^{10}+3 a^2 z^{10}+5 a^7 z^9+7 a^5 z^9+6 a^3 z^9+4 a z^9+5 a^8 z^8+a^6 z^8-9 a^4 z^8-a^2 z^8+4 z^8+3 a^9 z^7-10 a^7 z^7-20 a^5 z^7-13 a^3 z^7-3 a z^7+3 z^7 a^{-1} +a^{10} z^6-13 a^8 z^6-15 a^6 z^6+5 a^4 z^6-a^2 z^6+z^6 a^{-2} -6 z^6-8 a^9 z^5+7 a^7 z^5+24 a^5 z^5+10 a^3 z^5-7 a z^5-8 z^5 a^{-1} -3 a^{10} z^4+11 a^8 z^4+21 a^6 z^4+2 a^4 z^4-5 a^2 z^4-3 z^4 a^{-2} -3 z^4+5 a^9 z^3-5 a^7 z^3-12 a^5 z^3-2 a^3 z^3+6 a z^3+6 z^3 a^{-1} +2 a^{10} z^2-6 a^8 z^2-10 a^6 z^2+4 a^2 z^2+3 z^2 a^{-2} +5 z^2-a^9 z+2 a^7 z+4 a^5 z-2 a z-z a^{-1} +a^8+a^6-a^4-2 a^2- a^{-2} -1 }[/math] |
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