K12a227
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-5 q^{11}+12 q^{10}-21 q^9+30 q^8-37 q^7+39 q^6-36 q^5+29 q^4-19 q^3+11 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+26 t^2-56 t+71-56 t^{-1} +26 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-4 z^4+3 z^2+1 }[/math] |
| Determinant | 245 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} +z^4 a^{-4} -8 z^4 a^{-6} +z^4 a^{-8} +z^4 a^{-10} +z^2 a^{-2} +6 z^2 a^{-4} -9 z^2 a^{-6} +5 z^2 a^{-8} +4 a^{-4} -5 a^{-6} +3 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +7 z^{10} a^{-6} +15 z^{10} a^{-8} +8 z^{10} a^{-10} +11 z^9 a^{-5} +24 z^9 a^{-7} +26 z^9 a^{-9} +13 z^9 a^{-11} +9 z^8 a^{-4} +8 z^8 a^{-6} -5 z^8 a^{-8} +7 z^8 a^{-10} +11 z^8 a^{-12} +4 z^7 a^{-3} -18 z^7 a^{-5} -56 z^7 a^{-7} -59 z^7 a^{-9} -20 z^7 a^{-11} +5 z^7 a^{-13} +z^6 a^{-2} -19 z^6 a^{-4} -45 z^6 a^{-6} -44 z^6 a^{-8} -41 z^6 a^{-10} -21 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +10 z^5 a^{-5} +40 z^5 a^{-7} +36 z^5 a^{-9} +5 z^5 a^{-11} -8 z^5 a^{-13} -2 z^4 a^{-2} +18 z^4 a^{-4} +52 z^4 a^{-6} +52 z^4 a^{-8} +33 z^4 a^{-10} +12 z^4 a^{-12} -z^4 a^{-14} +3 z^3 a^{-3} -2 z^3 a^{-5} -9 z^3 a^{-7} -5 z^3 a^{-9} +2 z^3 a^{-11} +3 z^3 a^{-13} +z^2 a^{-2} -12 z^2 a^{-4} -26 z^2 a^{-6} -20 z^2 a^{-8} -9 z^2 a^{-10} -2 z^2 a^{-12} -z a^{-5} -z a^{-11} +4 a^{-4} +5 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
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