K12a83
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-17 q^9+24 q^8-30 q^7+33 q^6-30 q^5+25 q^4-17 q^3+10 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+20 t^2-48 t+63-48 t^{-1} +20 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+2 z^4+5 z^2+1 }[/math] |
| Determinant | 205 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} +z^4 a^{-2} -4 z^4 a^{-6} +5 z^4 a^{-8} +z^2 a^{-2} +3 z^2 a^{-4} -4 z^2 a^{-6} +9 z^2 a^{-8} -4 z^2 a^{-10} +2 a^{-4} -2 a^{-6} +4 a^{-8} -4 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +5 z^{10} a^{-6} +9 z^{10} a^{-8} +4 z^{10} a^{-10} +9 z^9 a^{-5} +20 z^9 a^{-7} +18 z^9 a^{-9} +7 z^9 a^{-11} +8 z^8 a^{-4} +8 z^8 a^{-6} +5 z^8 a^{-8} +12 z^8 a^{-10} +7 z^8 a^{-12} +4 z^7 a^{-3} -15 z^7 a^{-5} -46 z^7 a^{-7} -35 z^7 a^{-9} -4 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -17 z^6 a^{-4} -37 z^6 a^{-6} -46 z^6 a^{-8} -41 z^6 a^{-10} -13 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +8 z^5 a^{-5} +38 z^5 a^{-7} +16 z^5 a^{-9} -15 z^5 a^{-11} -9 z^5 a^{-13} -2 z^4 a^{-2} +13 z^4 a^{-4} +38 z^4 a^{-6} +52 z^4 a^{-8} +38 z^4 a^{-10} +7 z^4 a^{-12} -2 z^4 a^{-14} +4 z^3 a^{-3} -4 z^3 a^{-5} -16 z^3 a^{-7} +3 z^3 a^{-9} +18 z^3 a^{-11} +7 z^3 a^{-13} +z^2 a^{-2} -7 z^2 a^{-4} -16 z^2 a^{-6} -22 z^2 a^{-8} -17 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} +z a^{-5} +4 z a^{-7} -2 z a^{-9} -7 z a^{-11} -2 z a^{-13} +2 a^{-4} +2 a^{-6} +4 a^{-8} +4 a^{-10} + a^{-12} }[/math] |
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