K12a241
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-6+11 q^{-1} -15 q^{-2} +19 q^{-3} -19 q^{-4} +18 q^{-5} -15 q^{-6} +10 q^{-7} -6 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-13 t^2+29 t-37+29 t^{-1} -13 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+5 z^4+4 z^2+1 }[/math] |
| Determinant | 127 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-a^8+z^6 a^6+3 z^4 a^6+4 z^2 a^6+a^6+z^6 a^4+z^4 a^4-z^2 a^4-a^4+z^6 a^2+3 z^4 a^2+5 z^2 a^2+3 a^2-z^4-2 z^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+4 z^3 a^{11}-z a^{11}+3 z^8 a^{10}-12 z^6 a^{10}+13 z^4 a^{10}-4 z^2 a^{10}+4 z^9 a^9-14 z^7 a^9+13 z^5 a^9-5 z^3 a^9+z a^9+3 z^{10} a^8-6 z^8 a^8-4 z^6 a^8+8 z^4 a^8-z^2 a^8-a^8+z^{11} a^7+5 z^9 a^7-25 z^7 a^7+32 z^5 a^7-17 z^3 a^7+2 z a^7+6 z^{10} a^6-16 z^8 a^6+16 z^6 a^6-9 z^4 a^6+4 z^2 a^6-a^6+z^{11} a^5+5 z^9 a^5-17 z^7 a^5+21 z^5 a^5-10 z^3 a^5+z a^5+3 z^{10} a^4-3 z^8 a^4+5 z^6 a^4-8 z^4 a^4+6 z^2 a^4-a^4+4 z^9 a^3-3 z^7 a^3+z^5 a^3-2 z^3 a^3+2 z a^3+4 z^8 a^2-10 z^4 a^2+9 z^2 a^2-3 a^2+4 z^7 a-4 z^5 a-2 z^3 a+2 z a+3 z^6-6 z^4+4 z^2-1+z^5 a^{-1} -2 z^3 a^{-1} +z a^{-1} }[/math] |
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