K12a199
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-6 q^{11}+14 q^{10}-23 q^9+32 q^8-38 q^7+39 q^6-35 q^5+27 q^4-17 q^3+9 q^2-3 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} -8 z^4 a^{-6} +2 z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +3 z^2 a^{-4} -9 z^2 a^{-6} +8 z^2 a^{-8} -z^2 a^{-10} + a^{-2} +2 a^{-4} -5 a^{-6} +5 a^{-8} -2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +6 z^{10} a^{-6} +15 z^{10} a^{-8} +9 z^{10} a^{-10} +8 z^9 a^{-5} +21 z^9 a^{-7} +29 z^9 a^{-9} +16 z^9 a^{-11} +6 z^8 a^{-4} +5 z^8 a^{-6} -5 z^8 a^{-8} +10 z^8 a^{-10} +14 z^8 a^{-12} +3 z^7 a^{-3} -12 z^7 a^{-5} -51 z^7 a^{-7} -66 z^7 a^{-9} -24 z^7 a^{-11} +6 z^7 a^{-13} +z^6 a^{-2} -11 z^6 a^{-4} -32 z^6 a^{-6} -48 z^6 a^{-8} -54 z^6 a^{-10} -25 z^6 a^{-12} +z^6 a^{-14} -6 z^5 a^{-3} +9 z^5 a^{-5} +43 z^5 a^{-7} +36 z^5 a^{-9} +z^5 a^{-11} -7 z^5 a^{-13} -3 z^4 a^{-2} +9 z^4 a^{-4} +45 z^4 a^{-6} +64 z^4 a^{-8} +40 z^4 a^{-10} +9 z^4 a^{-12} +3 z^3 a^{-3} -4 z^3 a^{-5} -11 z^3 a^{-7} +4 z^3 a^{-11} +3 z^2 a^{-2} -6 z^2 a^{-4} -26 z^2 a^{-6} -29 z^2 a^{-8} -11 z^2 a^{-10} +z^2 a^{-12} -2 z a^{-9} -z a^{-11} +z a^{-13} - a^{-2} +2 a^{-4} +5 a^{-6} +5 a^{-8} +2 a^{-10} }[/math] |
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