K12a1151
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-3 q^4+7 q^3-11 q^2+16 q-19+20 q^{-1} -20 q^{-2} +16 q^{-3} -11 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-14 t^2+32 t-39+32 t^{-1} -14 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^4-6 z^2+1 }[/math] |
| Determinant | 135 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^6+a^6-2 z^4 a^4-3 z^2 a^4+z^6 a^2+z^4 a^2-z^2 a^2-a^2+z^6+z^4-z^2-2 z^4 a^{-2} -3 z^2 a^{-2} +z^2 a^{-4} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+4 z^{10} a^{-2} +10 z^{10}+9 a^3 z^9+6 a z^9+3 z^9 a^{-3} +9 a^4 z^8-11 a^2 z^8-16 z^8 a^{-2} +z^8 a^{-4} -37 z^8+8 a^5 z^7-21 a^3 z^7-40 a z^7-25 z^7 a^{-1} -14 z^7 a^{-3} +6 a^6 z^6-14 a^4 z^6-3 a^2 z^6+16 z^6 a^{-2} -5 z^6 a^{-4} +38 z^6+3 a^7 z^5-10 a^5 z^5+21 a^3 z^5+53 a z^5+39 z^5 a^{-1} +20 z^5 a^{-3} +a^8 z^4-7 a^6 z^4+6 a^4 z^4+11 a^2 z^4-2 z^4 a^{-2} +8 z^4 a^{-4} -13 z^4-2 a^7 z^3+5 a^5 z^3-18 a^3 z^3-32 a z^3-17 z^3 a^{-1} -10 z^3 a^{-3} -a^8 z^2+5 a^6 z^2-a^4 z^2-9 a^2 z^2-z^2 a^{-2} -5 z^2 a^{-4} +2 z^2+7 a^3 z+9 a z+3 z a^{-1} +z a^{-3} -a^6+a^2+ a^{-4} }[/math] |
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