K12a1265
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-13 q^3+20 q^2-24 q+26-25 q^{-1} +20 q^{-2} -14 q^{-3} +8 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+17 t^2-37 t+49-37 t^{-1} +17 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-7 z^4-5 z^2+1 }[/math] |
| Determinant | 165 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-2 a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} -5 z^4+2 a^4 z^2-3 a^2 z^2-2 z^2 a^{-2} +2 z^2 a^{-4} -4 z^2+2 a^4-2 a^2+ a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+5 z^{10} a^{-2} +10 z^{10}+7 a^3 z^9+5 a z^9+4 z^9 a^{-1} +6 z^9 a^{-3} +6 a^4 z^8-6 a^2 z^8-10 z^8 a^{-2} +5 z^8 a^{-4} -27 z^8+3 a^5 z^7-17 a^3 z^7-19 a z^7-16 z^7 a^{-1} -14 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-16 a^4 z^6-4 a^2 z^6+13 z^6 a^{-2} -12 z^6 a^{-4} +z^6 a^{-6} +39 z^6-7 a^5 z^5+18 a^3 z^5+26 a z^5+24 z^5 a^{-1} +15 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+16 a^4 z^4+14 a^2 z^4-9 z^4 a^{-2} +9 z^4 a^{-4} -3 z^4 a^{-6} -26 z^4+3 a^5 z^3-13 a^3 z^3-16 a z^3-15 z^3 a^{-1} -10 z^3 a^{-3} +5 z^3 a^{-5} +2 a^6 z^2-10 a^4 z^2-11 a^2 z^2-4 z^2 a^{-4} +2 z^2 a^{-6} +7 z^2+4 a^3 z+5 a z+3 z a^{-1} +2 z a^{-3} +2 a^4+2 a^2+ a^{-4} }[/math] |
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