K12a903
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+11 q^{10}-21 q^9+30 q^8-38 q^7+40 q^6-37 q^5+31 q^4-20 q^3+11 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+26 t^2-57 t+73-57 t^{-1} +26 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-4 z^4+2 z^2+1 }[/math] |
| Determinant | 249 |
| 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} -7 z^4 a^{-6} +z^4 a^{-10} +z^2 a^{-2} +5 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-10} +3 a^{-4} - a^{-6} -2 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-7} +3 z^{11} a^{-9} +9 z^{10} a^{-6} +19 z^{10} a^{-8} +10 z^{10} a^{-10} +12 z^9 a^{-5} +22 z^9 a^{-7} +23 z^9 a^{-9} +13 z^9 a^{-11} +9 z^8 a^{-4} -z^8 a^{-6} -27 z^8 a^{-8} -8 z^8 a^{-10} +9 z^8 a^{-12} +4 z^7 a^{-3} -21 z^7 a^{-5} -61 z^7 a^{-7} -67 z^7 a^{-9} -27 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -18 z^6 a^{-4} -28 z^6 a^{-6} -9 z^6 a^{-10} -17 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +14 z^5 a^{-5} +58 z^5 a^{-7} +72 z^5 a^{-9} +28 z^5 a^{-11} -7 z^5 a^{-13} -2 z^4 a^{-2} +16 z^4 a^{-4} +34 z^4 a^{-6} +13 z^4 a^{-8} +11 z^4 a^{-10} +12 z^4 a^{-12} -2 z^4 a^{-14} +3 z^3 a^{-3} -5 z^3 a^{-5} -29 z^3 a^{-7} -44 z^3 a^{-9} -20 z^3 a^{-11} +3 z^3 a^{-13} +z^2 a^{-2} -10 z^2 a^{-4} -15 z^2 a^{-6} -3 z^2 a^{-8} -4 z^2 a^{-10} -4 z^2 a^{-12} +z^2 a^{-14} +8 z a^{-7} +14 z a^{-9} +6 z a^{-11} +3 a^{-4} + a^{-6} -2 a^{-8} - a^{-10} }[/math] |
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