K12a616
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+5 q^{10}-14 q^9+24 q^8-34 q^7+41 q^6-42 q^5+39 q^4-30 q^3+20 q^2-10 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+32 t^2-55 t+65-55 t^{-1} +32 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+6 z^4+6 z^2+1 }[/math] |
| Determinant | 265 |
| 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} +3 z^4 a^{-6} -2 z^4 a^{-8} -3 z^2 a^{-2} +9 z^2 a^{-4} +2 z^2 a^{-6} -2 z^2 a^{-8} - a^{-2} +3 a^{-4} + a^{-6} -2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-5} +3 z^{11} a^{-7} +7 z^{10} a^{-4} +20 z^{10} a^{-6} +13 z^{10} a^{-8} +7 z^9 a^{-3} +18 z^9 a^{-5} +34 z^9 a^{-7} +23 z^9 a^{-9} +4 z^8 a^{-2} -5 z^8 a^{-4} -25 z^8 a^{-6} +7 z^8 a^{-8} +23 z^8 a^{-10} +z^7 a^{-1} -16 z^7 a^{-3} -59 z^7 a^{-5} -85 z^7 a^{-7} -29 z^7 a^{-9} +14 z^7 a^{-11} -12 z^6 a^{-2} -23 z^6 a^{-4} -24 z^6 a^{-6} -51 z^6 a^{-8} -33 z^6 a^{-10} +5 z^6 a^{-12} -3 z^5 a^{-1} +9 z^5 a^{-3} +49 z^5 a^{-5} +55 z^5 a^{-7} +3 z^5 a^{-9} -14 z^5 a^{-11} +z^5 a^{-13} +13 z^4 a^{-2} +36 z^4 a^{-4} +36 z^4 a^{-6} +31 z^4 a^{-8} +17 z^4 a^{-10} -z^4 a^{-12} +3 z^3 a^{-1} +2 z^3 a^{-3} -11 z^3 a^{-5} -14 z^3 a^{-7} +3 z^3 a^{-9} +7 z^3 a^{-11} -6 z^2 a^{-2} -18 z^2 a^{-4} -9 z^2 a^{-6} -z^2 a^{-8} -4 z^2 a^{-10} -z a^{-1} -2 z a^{-3} -z a^{-5} +3 z a^{-7} -3 z a^{-11} + a^{-2} +3 a^{-4} - a^{-6} -2 a^{-8} }[/math] |
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