K12a1240
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^9+3 q^8-5 q^7+8 q^6-11 q^5+13 q^4-14 q^3+13 q^2-11 q+9-5 q^{-1} +3 q^{-2} - q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+14 t^2-16 t+17-16 t^{-1} +14 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+6 z^4+1 }[/math] |
| Determinant | 97 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8 a^{-4} +5 z^6 a^{-2} +5 z^6 a^{-4} -z^6 a^{-6} -z^6+7 z^4 a^{-2} +7 z^4 a^{-4} -4 z^4 a^{-6} -4 z^4+3 z^2 a^{-2} +3 z^2 a^{-4} -3 z^2 a^{-6} -3 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +9 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10}+a z^9-7 z^9 a^{-1} +z^9 a^{-3} +9 z^9 a^{-5} -49 z^8 a^{-2} -20 z^8 a^{-4} +10 z^8 a^{-6} -19 z^8-6 a z^7-5 z^7 a^{-1} -38 z^7 a^{-3} -30 z^7 a^{-5} +9 z^7 a^{-7} +85 z^6 a^{-2} +9 z^6 a^{-4} -28 z^6 a^{-6} +7 z^6 a^{-8} +41 z^6+12 a z^5+35 z^5 a^{-1} +68 z^5 a^{-3} +22 z^5 a^{-5} -18 z^5 a^{-7} +5 z^5 a^{-9} -55 z^4 a^{-2} +8 z^4 a^{-4} +17 z^4 a^{-6} -8 z^4 a^{-8} +3 z^4 a^{-10} -35 z^4-9 a z^3-30 z^3 a^{-1} -33 z^3 a^{-3} -2 z^3 a^{-5} +6 z^3 a^{-7} -3 z^3 a^{-9} +z^3 a^{-11} +12 z^2 a^{-2} -z^2 a^{-4} -3 z^2 a^{-6} -z^2 a^{-10} +9 z^2+2 a z+5 z a^{-1} +3 z a^{-3} -z a^{-5} -z a^{-7} +1 }[/math] |
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