K12a286
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-12 q^5+21 q^4-29 q^3+35 q^2-37 q+34-27 q^{-1} +18 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+20 t^2-55 t+77-55 t^{-1} +20 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+2 z^4-2 z^2+1 }[/math] |
| Determinant | 233 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6+2 a^2 z^4-4 z^4 a^{-2} +3 z^4 a^{-4} +z^4-a^4 z^2+a^2 z^2-5 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} +z^2+a^2- a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +19 z^{10} a^{-2} +9 z^{10} a^{-4} +10 z^{10}+14 a z^9+24 z^9 a^{-1} +20 z^9 a^{-3} +10 z^9 a^{-5} +12 a^2 z^8-33 z^8 a^{-2} -12 z^8 a^{-4} +5 z^8 a^{-6} -4 z^8+8 a^3 z^7-22 a z^7-80 z^7 a^{-1} -78 z^7 a^{-3} -27 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-15 a^2 z^6-13 z^6 a^{-2} -21 z^6 a^{-4} -13 z^6 a^{-6} -24 z^6+a^5 z^5-9 a^3 z^5+17 a z^5+82 z^5 a^{-1} +77 z^5 a^{-3} +20 z^5 a^{-5} -2 z^5 a^{-7} -5 a^4 z^4+6 a^2 z^4+41 z^4 a^{-2} +32 z^4 a^{-4} +10 z^4 a^{-6} +30 z^4-a^5 z^3+3 a^3 z^3-7 a z^3-34 z^3 a^{-1} -30 z^3 a^{-3} -6 z^3 a^{-5} +z^3 a^{-7} +2 a^4 z^2+a^2 z^2-17 z^2 a^{-2} -12 z^2 a^{-4} -3 z^2 a^{-6} -9 z^2+a z+5 z a^{-1} +5 z a^{-3} +z a^{-5} -a^2+ a^{-2} + a^{-4} }[/math] |
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