K12a360
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-12 q^5+20 q^4-28 q^3+34 q^2-35 q+33-26 q^{-1} +17 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+20 t^2-53 t+73-53 t^{-1} +20 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+2 z^4+1 }[/math] |
| Determinant | 225 |
| 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^2-4 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} +2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +18 z^{10} a^{-2} +9 z^{10} a^{-4} +9 z^{10}+12 a z^9+19 z^9 a^{-1} +17 z^9 a^{-3} +10 z^9 a^{-5} +11 a^2 z^8-34 z^8 a^{-2} -15 z^8 a^{-4} +5 z^8 a^{-6} -3 z^8+8 a^3 z^7-13 a z^7-59 z^7 a^{-1} -67 z^7 a^{-3} -28 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-12 a^2 z^6-2 z^6 a^{-2} -11 z^6 a^{-4} -13 z^6 a^{-6} -20 z^6+a^5 z^5-10 a^3 z^5-a z^5+46 z^5 a^{-1} +59 z^5 a^{-3} +21 z^5 a^{-5} -2 z^5 a^{-7} -5 a^4 z^4+3 a^2 z^4+26 z^4 a^{-2} +20 z^4 a^{-4} +9 z^4 a^{-6} +23 z^4-a^5 z^3+5 a^3 z^3+8 a z^3-5 z^3 a^{-1} -13 z^3 a^{-3} -5 z^3 a^{-5} +z^3 a^{-7} +2 a^4 z^2-10 z^2 a^{-2} -6 z^2 a^{-4} -2 z^2 a^{-6} -8 z^2-a^3 z-3 a z-3 z a^{-1} -z a^{-3} +1 }[/math] |
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