K12a989
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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}+4 z^3 a^{11}+3 z^8 a^{10}-11 z^6 a^{10}+11 z^4 a^{10}-2 z^2 a^{10}+5 z^9 a^9-18 z^7 a^9+24 z^5 a^9-18 z^3 a^9+6 z a^9+5 z^{10} a^8-15 z^8 a^8+19 z^6 a^8-17 z^4 a^8+6 z^2 a^8-a^8+2 z^{11} a^7+5 z^9 a^7-30 z^7 a^7+48 z^5 a^7-39 z^3 a^7+9 z a^7+11 z^{10} a^6-29 z^8 a^6+32 z^6 a^6-20 z^4 a^6+4 z^2 a^6+2 z^{11} a^5+10 z^9 a^5-32 z^7 a^5+33 z^5 a^5-15 z^3 a^5+3 z a^5+6 z^{10} a^4-20 z^6 a^4+25 z^4 a^4-9 z^2 a^4+2 a^4+10 z^9 a^3-13 z^7 a^3+z^5 a^3+7 z^3 a^3-z a^3+11 z^8 a^2-18 z^6 a^2+12 z^4 a^2-4 z^2 a^2+8 z^7 a-11 z^5 a+4 z^3 a-z a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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