K12a501
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-11 q^6+18 q^5-25 q^4+30 q^3-31 q^2+28 q-22+15 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-23 t^2+43 t-51+43 t^{-1} -23 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-z^4-2 z^2+1 }[/math] |
| Determinant | 199 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-12 z^4 a^{-2} +6 z^4 a^{-4} -z^4 a^{-6} +7 z^4-2 a^2 z^2-13 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +8 z^2-4 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +9 z^{10} a^{-2} +5 z^{10} a^{-4} +4 z^{10}+6 a z^9+16 z^9 a^{-1} +21 z^9 a^{-3} +11 z^9 a^{-5} +4 a^2 z^8+17 z^8 a^{-4} +14 z^8 a^{-6} +z^8+a^3 z^7-18 a z^7-51 z^7 a^{-1} -47 z^7 a^{-3} -4 z^7 a^{-5} +11 z^7 a^{-7} -14 a^2 z^6-48 z^6 a^{-2} -53 z^6 a^{-4} -18 z^6 a^{-6} +5 z^6 a^{-8} -32 z^6-3 a^3 z^5+16 a z^5+50 z^5 a^{-1} +29 z^5 a^{-3} -17 z^5 a^{-5} -14 z^5 a^{-7} +z^5 a^{-9} +15 a^2 z^4+63 z^4 a^{-2} +42 z^4 a^{-4} +5 z^4 a^{-6} -4 z^4 a^{-8} +45 z^4+2 a^3 z^3-5 a z^3-20 z^3 a^{-1} -6 z^3 a^{-3} +11 z^3 a^{-5} +4 z^3 a^{-7} -5 a^2 z^2-29 z^2 a^{-2} -13 z^2 a^{-4} -21 z^2+a z+3 z a^{-1} +z a^{-3} -z a^{-5} +4 a^{-2} +2 a^{-4} +3 }[/math] |
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