K12a317
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-13+23 q^{-1} -32 q^{-2} +40 q^{-3} -41 q^{-4} +38 q^{-5} -30 q^{-6} +20 q^{-7} -11 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^3-25 t^2+60 t-79+60 t^{-1} -25 t^{-2} +5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^6+5 z^4+5 z^2+1 }[/math] |
| Determinant | 259 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-z^2 a^8-a^8+z^6 a^6-z^2 a^6-a^6+3 z^6 a^4+8 z^4 a^4+10 z^2 a^4+4 a^4+z^6 a^2-z^4 a^2-3 z^2 a^2-a^2-z^4 }[/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}-11 z^6 a^{10}+10 z^4 a^{10}-3 z^2 a^{10}+8 z^9 a^9-21 z^7 a^9+19 z^5 a^9-9 z^3 a^9+3 z a^9+8 z^{10} a^8-11 z^8 a^8-8 z^6 a^8+13 z^4 a^8-2 z^2 a^8-a^8+3 z^{11} a^7+19 z^9 a^7-66 z^7 a^7+62 z^5 a^7-24 z^3 a^7+4 z a^7+20 z^{10} a^6-28 z^8 a^6-18 z^6 a^6+33 z^4 a^6-11 z^2 a^6+a^6+3 z^{11} a^5+32 z^9 a^5-84 z^7 a^5+58 z^5 a^5-11 z^3 a^5-z a^5+12 z^{10} a^4+8 z^8 a^4-57 z^6 a^4+50 z^4 a^4-18 z^2 a^4+4 a^4+21 z^9 a^3-27 z^7 a^3+4 z^5 a^3+5 z^3 a^3-2 z a^3+21 z^8 a^2-31 z^6 a^2+18 z^4 a^2-6 z^2 a^2+a^2+13 z^7 a-13 z^5 a+4 z^3 a-z a+5 z^6-2 z^4+z^5 a^{-1} }[/math] |
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