K12a513
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+16 q^{-1} -22 q^{-2} +27 q^{-3} -27 q^{-4} +25 q^{-5} -20 q^{-6} +13 q^{-7} -7 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-18 t^2+40 t-51+40 t^{-1} -18 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+6 z^4+4 z^2+1 }[/math] |
| Determinant | 175 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-a^8+z^6 a^6+2 z^4 a^6+2 z^2 a^6+2 z^6 a^4+5 z^4 a^4+5 z^2 a^4+2 a^4+z^6 a^2+z^4 a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-11 z^6 a^{10}+13 z^4 a^{10}-5 z^2 a^{10}+4 z^9 a^9-10 z^7 a^9+4 z^5 a^9+4 z^3 a^9-2 z a^9+3 z^{10} a^8-17 z^6 a^8+18 z^4 a^8-3 z^2 a^8-a^8+z^{11} a^7+9 z^9 a^7-23 z^7 a^7+9 z^5 a^7+5 z^3 a^7-3 z a^7+7 z^{10} a^6-2 z^8 a^6-22 z^6 a^6+19 z^4 a^6-4 z^2 a^6+z^{11} a^5+13 z^9 a^5-21 z^7 a^5-3 z^5 a^5+13 z^3 a^5-5 z a^5+4 z^{10} a^4+11 z^8 a^4-32 z^6 a^4+24 z^4 a^4-9 z^2 a^4+2 a^4+8 z^9 a^3-z^7 a^3-16 z^5 a^3+14 z^3 a^3-3 z a^3+10 z^8 a^2-12 z^6 a^2+5 z^4 a^2-z^2 a^2+8 z^7 a-11 z^5 a+6 z^3 a-z a+4 z^6-5 z^4+2 z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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