K12a863
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-7+12 q^{-1} -16 q^{-2} +19 q^{-3} -20 q^{-4} +18 q^{-5} -14 q^{-6} +10 q^{-7} -6 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-14 t^2+30 t-37+30 t^{-1} -14 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+4 z^4+z^2+1 }[/math] |
| Determinant | 131 |
| 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+2 a^6+z^6 a^4+z^4 a^4-z^2 a^4-a^4+z^6 a^2+2 z^4 a^2+z^2 a^2-z^4-z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+3 z^3 a^{11}+3 z^8 a^{10}-12 z^6 a^{10}+11 z^4 a^{10}-3 z^2 a^{10}+5 z^9 a^9-21 z^7 a^9+26 z^5 a^9-16 z^3 a^9+4 z a^9+5 z^{10} a^8-20 z^8 a^8+25 z^6 a^8-16 z^4 a^8+5 z^2 a^8-a^8+2 z^{11} a^7+z^9 a^7-30 z^7 a^7+57 z^5 a^7-38 z^3 a^7+8 z a^7+10 z^{10} a^6-42 z^8 a^6+65 z^6 a^6-42 z^4 a^6+14 z^2 a^6-2 a^6+2 z^{11} a^5+2 z^9 a^5-25 z^7 a^5+47 z^5 a^5-27 z^3 a^5+5 z a^5+5 z^{10} a^4-13 z^8 a^4+18 z^6 a^4-12 z^4 a^4+6 z^2 a^4-a^4+6 z^9 a^3-11 z^7 a^3+10 z^5 a^3-6 z^3 a^3+z a^3+6 z^8 a^2-6 z^6 a^2-4 z^4 a^2+2 z^2 a^2+6 z^7 a-9 z^5 a+z^3 a+4 z^6-7 z^4+2 z^2+1+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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