K12a400
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+4 q^9-10 q^8+17 q^7-24 q^6+30 q^5-32 q^4+30 q^3-24 q^2+17 q-9+4 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-18 t^2+48 t-65+48 t^{-1} -18 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+3 z^2+1 }[/math] |
| Determinant | 203 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +z^4 a^{-2} +5 z^4 a^{-4} -5 z^4 a^{-6} -z^4+z^2 a^{-2} +8 z^2 a^{-4} -9 z^2 a^{-6} +4 z^2 a^{-8} -z^2+4 a^{-4} -5 a^{-6} +3 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-5} +2 z^{11} a^{-7} +8 z^{10} a^{-4} +14 z^{10} a^{-6} +6 z^{10} a^{-8} +13 z^9 a^{-3} +22 z^9 a^{-5} +16 z^9 a^{-7} +7 z^9 a^{-9} +12 z^8 a^{-2} -z^8 a^{-4} -23 z^8 a^{-6} -6 z^8 a^{-8} +4 z^8 a^{-10} +8 z^7 a^{-1} -25 z^7 a^{-3} -77 z^7 a^{-5} -64 z^7 a^{-7} -19 z^7 a^{-9} +z^7 a^{-11} -20 z^6 a^{-2} -34 z^6 a^{-4} -21 z^6 a^{-6} -23 z^6 a^{-8} -12 z^6 a^{-10} +4 z^6+a z^5-10 z^5 a^{-1} +23 z^5 a^{-3} +89 z^5 a^{-5} +71 z^5 a^{-7} +13 z^5 a^{-9} -3 z^5 a^{-11} +14 z^4 a^{-2} +53 z^4 a^{-4} +57 z^4 a^{-6} +34 z^4 a^{-8} +11 z^4 a^{-10} -5 z^4-a z^3+2 z^3 a^{-1} -10 z^3 a^{-3} -39 z^3 a^{-5} -34 z^3 a^{-7} -5 z^3 a^{-9} +3 z^3 a^{-11} -5 z^2 a^{-2} -26 z^2 a^{-4} -32 z^2 a^{-6} -17 z^2 a^{-8} -5 z^2 a^{-10} +z^2+2 z a^{-3} +5 z a^{-5} +6 z a^{-7} +2 z a^{-9} -z a^{-11} +4 a^{-4} +5 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
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