K12a609
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-10+19 q^{-1} -27 q^{-2} +34 q^{-3} -35 q^{-4} +33 q^{-5} -27 q^{-6} +18 q^{-7} -10 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^3-23 t^2+51 t-65+51 t^{-1} -23 t^{-2} +5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^6+7 z^4+4 z^2+1 }[/math] |
| Determinant | 223 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-z^2 a^8+z^6 a^6-3 z^2 a^6-3 a^6+3 z^6 a^4+9 z^4 a^4+11 z^2 a^4+5 a^4+z^6 a^2-2 z^2 a^2-a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-3 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+4 z^8 a^{10}-12 z^6 a^{10}+12 z^4 a^{10}-4 z^2 a^{10}+7 z^9 a^9-18 z^7 a^9+13 z^5 a^9-2 z^3 a^9+6 z^{10} a^8-4 z^8 a^8-21 z^6 a^8+24 z^4 a^8-6 z^2 a^8+2 z^{11} a^7+17 z^9 a^7-53 z^7 a^7+40 z^5 a^7-9 z^3 a^7-z a^7+14 z^{10} a^6-13 z^8 a^6-32 z^6 a^6+41 z^4 a^6-17 z^2 a^6+3 a^6+2 z^{11} a^5+24 z^9 a^5-60 z^7 a^5+39 z^5 a^5-5 z^3 a^5-3 z a^5+8 z^{10} a^4+9 z^8 a^4-49 z^6 a^4+52 z^4 a^4-24 z^2 a^4+5 a^4+14 z^9 a^3-17 z^7 a^3+3 z^5 a^3+6 z^3 a^3-2 z a^3+14 z^8 a^2-22 z^6 a^2+19 z^4 a^2-8 z^2 a^2+a^2+9 z^7 a-11 z^5 a+6 z^3 a-z a+4 z^6-4 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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