K12a837
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-7 q^3+12 q^2-17 q+22-22 q^{-1} +21 q^{-2} -17 q^{-3} +12 q^{-4} -7 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+18 t^2-28 t+33-28 t^{-1} +18 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+10 z^4+4 z^2+1 }[/math] |
| Determinant | 145 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+5 a^2 z^6-z^6 a^{-2} +5 z^6-4 a^4 z^4+9 a^2 z^4-4 z^4 a^{-2} +9 z^4-5 a^4 z^2+7 a^2 z^2-5 z^2 a^{-2} +7 z^2-2 a^4+2 a^2-2 a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+7 a^2 z^{10}+4 z^{10}+4 a^5 z^9+7 a^3 z^9+10 a z^9+7 z^9 a^{-1} +3 a^6 z^8-3 a^4 z^8-15 a^2 z^8+8 z^8 a^{-2} -z^8+a^7 z^7-11 a^5 z^7-26 a^3 z^7-34 a z^7-14 z^7 a^{-1} +6 z^7 a^{-3} -11 a^6 z^6-9 a^4 z^6+11 a^2 z^6-20 z^6 a^{-2} +3 z^6 a^{-4} -14 z^6-4 a^7 z^5+5 a^5 z^5+27 a^3 z^5+43 a z^5+11 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} +12 a^6 z^4+6 a^4 z^4-9 a^2 z^4+24 z^4 a^{-2} -5 z^4 a^{-4} +26 z^4+5 a^7 z^3+2 a^5 z^3-18 a^3 z^3-23 a z^3+4 z^3 a^{-1} +10 z^3 a^{-3} -2 z^3 a^{-5} -4 a^6 z^2+3 a^4 z^2+5 a^2 z^2-11 z^2 a^{-2} -13 z^2-2 a^7 z+5 a^3 z+3 a z-3 z a^{-1} -3 z a^{-3} -2 a^4-2 a^2+2 a^{-2} +3 }[/math] |
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