K12a26
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-7 q^{-1} +12 q^{-2} -17 q^{-3} +21 q^{-4} -22 q^{-5} +21 q^{-6} -17 q^{-7} +12 q^{-8} -7 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+20 t^2-29 t+31-29 t^{-1} +20 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-2 z^4+4 z^2+1 }[/math] |
| Determinant | 145 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^{10}-2 a^{10}+3 z^4 a^8+9 z^2 a^8+5 a^8-3 z^6 a^6-12 z^4 a^6-14 z^2 a^6-6 a^6+z^8 a^4+5 z^6 a^4+10 z^4 a^4+11 z^2 a^4+4 a^4-z^6 a^2-3 z^4 a^2-z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-5 z^4 a^{12}+2 z^2 a^{12}+5 z^7 a^{11}-7 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+6 z^8 a^{10}-8 z^6 a^{10}+6 z^4 a^{10}-5 z^2 a^{10}+2 a^{10}+5 z^9 a^9-3 z^7 a^9-3 z^5 a^9+3 z^3 a^9+3 z^{10} a^8+4 z^8 a^8-20 z^6 a^8+28 z^4 a^8-19 z^2 a^8+5 a^8+z^{11} a^7+9 z^9 a^7-29 z^7 a^7+35 z^5 a^7-20 z^3 a^7+4 z a^7+7 z^{10} a^6-12 z^8 a^6-11 z^6 a^6+37 z^4 a^6-28 z^2 a^6+6 a^6+z^{11} a^5+10 z^9 a^5-44 z^7 a^5+55 z^5 a^5-26 z^3 a^5+3 z a^5+4 z^{10} a^4-6 z^8 a^4-17 z^6 a^4+34 z^4 a^4-19 z^2 a^4+4 a^4+6 z^9 a^3-22 z^7 a^3+22 z^5 a^3-7 z^3 a^3+z a^3+4 z^8 a^2-15 z^6 a^2+14 z^4 a^2-3 z^2 a^2+z^7 a-3 z^5 a+z^3 a }[/math] |
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