K12a36
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-4 q^{12}+9 q^{11}-16 q^{10}+21 q^9-24 q^8+25 q^7-22 q^6+17 q^5-11 q^4+6 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-21 t^2+30 t-33+30 t^{-1} -21 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-z^4+4 z^2+1 }[/math] |
| Determinant | 159 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -5 z^6 a^{-6} -3 z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-4} -10 z^4 a^{-6} +2 z^4 a^{-8} +2 z^4 a^{-10} +8 z^2 a^{-4} -12 z^2 a^{-6} +11 z^2 a^{-8} -3 z^2 a^{-10} +4 a^{-4} -7 a^{-6} +8 a^{-8} -5 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +7 z^{10} a^{-8} +5 z^{10} a^{-10} +2 z^9 a^{-5} +5 z^9 a^{-7} +15 z^9 a^{-9} +12 z^9 a^{-11} +z^8 a^{-4} -3 z^8 a^{-6} -10 z^8 a^{-8} +11 z^8 a^{-10} +17 z^8 a^{-12} -9 z^7 a^{-5} -27 z^7 a^{-7} -45 z^7 a^{-9} -12 z^7 a^{-11} +15 z^7 a^{-13} -6 z^6 a^{-4} -14 z^6 a^{-6} -29 z^6 a^{-8} -60 z^6 a^{-10} -30 z^6 a^{-12} +9 z^6 a^{-14} +13 z^5 a^{-5} +31 z^5 a^{-7} +22 z^5 a^{-9} -21 z^5 a^{-11} -21 z^5 a^{-13} +4 z^5 a^{-15} +13 z^4 a^{-4} +37 z^4 a^{-6} +61 z^4 a^{-8} +61 z^4 a^{-10} +17 z^4 a^{-12} -6 z^4 a^{-14} +z^4 a^{-16} -6 z^3 a^{-5} -9 z^3 a^{-7} +11 z^3 a^{-9} +26 z^3 a^{-11} +11 z^3 a^{-13} -z^3 a^{-15} -12 z^2 a^{-4} -29 z^2 a^{-6} -38 z^2 a^{-8} -27 z^2 a^{-10} -5 z^2 a^{-12} +z^2 a^{-14} -6 z a^{-9} -8 z a^{-11} -2 z a^{-13} +4 a^{-4} +7 a^{-6} +8 a^{-8} +5 a^{-10} + a^{-12} }[/math] |
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