K12a114
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-17 q^9+25 q^8-30 q^7+32 q^6-30 q^5+24 q^4-16 q^3+9 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+21 t^2-46 t+59-46 t^{-1} +21 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-3 z^4+2 z^2+1 }[/math] |
| Determinant | 201 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} +z^4 a^{-2} -10 z^4 a^{-6} +6 z^4 a^{-8} +2 z^2 a^{-2} +4 z^2 a^{-4} -14 z^2 a^{-6} +14 z^2 a^{-8} -4 z^2 a^{-10} + a^{-2} +3 a^{-4} -8 a^{-6} +9 a^{-8} -5 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +4 z^{10} a^{-6} +8 z^{10} a^{-8} +4 z^{10} a^{-10} +7 z^9 a^{-5} +17 z^9 a^{-7} +17 z^9 a^{-9} +7 z^9 a^{-11} +6 z^8 a^{-4} +11 z^8 a^{-6} +11 z^8 a^{-8} +13 z^8 a^{-10} +7 z^8 a^{-12} +3 z^7 a^{-3} -9 z^7 a^{-5} -32 z^7 a^{-7} -27 z^7 a^{-9} -3 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -12 z^6 a^{-4} -44 z^6 a^{-6} -62 z^6 a^{-8} -45 z^6 a^{-10} -13 z^6 a^{-12} +z^6 a^{-14} -6 z^5 a^{-3} +2 z^5 a^{-5} +13 z^5 a^{-7} -4 z^5 a^{-9} -18 z^5 a^{-11} -9 z^5 a^{-13} -3 z^4 a^{-2} +11 z^4 a^{-4} +56 z^4 a^{-6} +77 z^4 a^{-8} +45 z^4 a^{-10} +8 z^4 a^{-12} -2 z^4 a^{-14} +3 z^3 a^{-3} +z^3 a^{-5} +5 z^3 a^{-7} +21 z^3 a^{-9} +21 z^3 a^{-11} +7 z^3 a^{-13} +3 z^2 a^{-2} -8 z^2 a^{-4} -35 z^2 a^{-6} -43 z^2 a^{-8} -23 z^2 a^{-10} -3 z^2 a^{-12} +z^2 a^{-14} -z a^{-5} -3 z a^{-7} -7 z a^{-9} -7 z a^{-11} -2 z a^{-13} - a^{-2} +3 a^{-4} +8 a^{-6} +9 a^{-8} +5 a^{-10} + a^{-12} }[/math] |
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