K12a1246
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-7 q^6+12 q^5-17 q^4+21 q^3-22 q^2+21 q-16+12 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+10 t^3-18 t^2+25 t-27+25 t^{-1} -18 t^{-2} +10 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+13 z^6+12 z^4+4 z^2+1 }[/math] |
| Determinant | 143 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +8 z^8 a^{-2} -z^8 a^{-4} -z^8+25 z^6 a^{-2} -6 z^6 a^{-4} -6 z^6+38 z^4 a^{-2} -13 z^4 a^{-4} -13 z^4+28 z^2 a^{-2} -12 z^2 a^{-4} -12 z^2+8 a^{-2} -4 a^{-4} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +10 z^{10} a^{-2} +6 z^{10} a^{-4} +4 z^{10}+4 a z^9+4 z^9 a^{-3} +8 z^9 a^{-5} +3 a^2 z^8-39 z^8 a^{-2} -17 z^8 a^{-4} +8 z^8 a^{-6} -11 z^8+a^3 z^7-11 a z^7-13 z^7 a^{-1} -29 z^7 a^{-3} -22 z^7 a^{-5} +6 z^7 a^{-7} -11 a^2 z^6+72 z^6 a^{-2} +27 z^6 a^{-4} -20 z^6 a^{-6} +3 z^6 a^{-8} +11 z^6-4 a^3 z^5+3 a z^5+21 z^5 a^{-1} +57 z^5 a^{-3} +29 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4-75 z^4 a^{-2} -21 z^4 a^{-4} +21 z^4 a^{-6} -5 z^4 a^{-8} -17 z^4+5 a^3 z^3+5 a z^3-21 z^3 a^{-1} -45 z^3 a^{-3} -13 z^3 a^{-5} +9 z^3 a^{-7} -2 z^3 a^{-9} -3 a^2 z^2+37 z^2 a^{-2} +13 z^2 a^{-4} -6 z^2 a^{-6} +15 z^2-2 a^3 z-a z+7 z a^{-1} +11 z a^{-3} +3 z a^{-5} -2 z a^{-7} -8 a^{-2} -4 a^{-4} -3 }[/math] |
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