K12a618
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+5 q^{10}-13 q^9+23 q^8-33 q^7+39 q^6-41 q^5+38 q^4-29 q^3+20 q^2-10 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+31 t^2-53 t+63-53 t^{-1} +31 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+5 z^4+4 z^2+1 }[/math] |
| Determinant | 257 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +4 z^6 a^{-4} +3 z^6 a^{-6} -z^6 a^{-8} -3 z^4 a^{-2} +8 z^4 a^{-4} +2 z^4 a^{-6} -2 z^4 a^{-8} -3 z^2 a^{-2} +10 z^2 a^{-4} -2 z^2 a^{-6} -z^2 a^{-8} - a^{-2} +5 a^{-4} -3 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-5} +3 z^{11} a^{-7} +7 z^{10} a^{-4} +19 z^{10} a^{-6} +12 z^{10} a^{-8} +7 z^9 a^{-3} +16 z^9 a^{-5} +30 z^9 a^{-7} +21 z^9 a^{-9} +4 z^8 a^{-2} -6 z^8 a^{-4} -24 z^8 a^{-6} +7 z^8 a^{-8} +21 z^8 a^{-10} +z^7 a^{-1} -16 z^7 a^{-3} -51 z^7 a^{-5} -73 z^7 a^{-7} -26 z^7 a^{-9} +13 z^7 a^{-11} -12 z^6 a^{-2} -20 z^6 a^{-4} -23 z^6 a^{-6} -50 z^6 a^{-8} -30 z^6 a^{-10} +5 z^6 a^{-12} -3 z^5 a^{-1} +8 z^5 a^{-3} +34 z^5 a^{-5} +39 z^5 a^{-7} +2 z^5 a^{-9} -13 z^5 a^{-11} +z^5 a^{-13} +13 z^4 a^{-2} +32 z^4 a^{-4} +37 z^4 a^{-6} +36 z^4 a^{-8} +16 z^4 a^{-10} -2 z^4 a^{-12} +3 z^3 a^{-1} +4 z^3 a^{-3} +2 z^3 a^{-5} +z^3 a^{-7} +5 z^3 a^{-9} +5 z^3 a^{-11} -6 z^2 a^{-2} -18 z^2 a^{-4} -15 z^2 a^{-6} -7 z^2 a^{-8} -4 z^2 a^{-10} -z a^{-1} -3 z a^{-3} -6 z a^{-5} -4 z a^{-7} -z a^{-9} -z a^{-11} + a^{-2} +5 a^{-4} +3 a^{-6} }[/math] |
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