K12a230
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-12+21 q^{-1} -29 q^{-2} +36 q^{-3} -37 q^{-4} +34 q^{-5} -27 q^{-6} +18 q^{-7} -10 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-20 t^2+56 t-77+56 t^{-1} -20 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-2 z^4+3 z^2+1 }[/math] |
| Determinant | 235 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+4 z^2 a^8+3 a^8-5 z^4 a^6-8 z^2 a^6-5 a^6+2 z^6 a^4+4 z^4 a^4+7 z^2 a^4+4 a^4+z^6 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}-12 z^6 a^{10}+12 z^4 a^{10}-5 z^2 a^{10}+a^{10}+7 z^9 a^9-18 z^7 a^9+13 z^5 a^9-3 z^3 a^9+z a^9+6 z^{10} a^8-3 z^8 a^8-27 z^6 a^8+38 z^4 a^8-18 z^2 a^8+3 a^8+2 z^{11} a^7+19 z^9 a^7-63 z^7 a^7+60 z^5 a^7-23 z^3 a^7+3 z a^7+15 z^{10} a^6-13 z^8 a^6-42 z^6 a^6+63 z^4 a^6-30 z^2 a^6+5 a^6+2 z^{11} a^5+29 z^9 a^5-76 z^7 a^5+60 z^5 a^5-19 z^3 a^5+2 z a^5+9 z^{10} a^4+12 z^8 a^4-58 z^6 a^4+53 z^4 a^4-20 z^2 a^4+4 a^4+17 z^9 a^3-20 z^7 a^3+2 z^5 a^3+z^3 a^3+z a^3+18 z^8 a^2-26 z^6 a^2+13 z^4 a^2-3 z^2 a^2+12 z^7 a-13 z^5 a+3 z^3 a+5 z^6-3 z^4+z^5 a^{-1} }[/math] |
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