K12a835
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+2 q^3-4 q^2+6 q-7+10 q^{-1} -10 q^{-2} +10 q^{-3} -8 q^{-4} +6 q^{-5} -4 q^{-6} +2 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-3 t^4+6 t^3-9 t^2+11 t-11+11 t^{-1} -9 t^{-2} +6 t^{-3} -3 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+7 z^8+17 z^6+17 z^4+6 z^2+1 }[/math] |
| Determinant | 71 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+9 a^2 z^8-z^8-7 a^4 z^6+31 a^2 z^6-7 z^6-17 a^4 z^4+51 a^2 z^4-17 z^4-17 a^4 z^2+40 a^2 z^2-17 z^2-6 a^4+12 a^2-5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+2 a^4 z^{10}+5 a^2 z^{10}+3 z^{10}+2 a^5 z^9-2 a^3 z^9-a z^9+3 z^9 a^{-1} +2 a^6 z^8-9 a^4 z^8-30 a^2 z^8+2 z^8 a^{-2} -17 z^8+2 a^7 z^7-6 a^5 z^7-6 a^3 z^7-14 a z^7-15 z^7 a^{-1} +z^7 a^{-3} +2 a^8 z^6-4 a^6 z^6+20 a^4 z^6+72 a^2 z^6-9 z^6 a^{-2} +37 z^6+a^9 z^5-3 a^7 z^5+9 a^5 z^5+25 a^3 z^5+40 a z^5+23 z^5 a^{-1} -5 z^5 a^{-3} -5 a^8 z^4+4 a^6 z^4-23 a^4 z^4-85 a^2 z^4+9 z^4 a^{-2} -44 z^4-3 a^9 z^3-a^7 z^3-4 a^5 z^3-25 a^3 z^3-41 a z^3-16 z^3 a^{-1} +6 z^3 a^{-3} +2 a^8 z^2-3 a^6 z^2+20 a^4 z^2+50 a^2 z^2-z^2 a^{-2} +24 z^2+2 a^9 z+a^5 z+10 a^3 z+12 a z+4 z a^{-1} -z a^{-3} -6 a^4-12 a^2-5 }[/math] |
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