K12a631
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-20 q^3+28 q^2-34 q+36-32 q^{-1} +26 q^{-2} -17 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+22 t^2-52 t+69-52 t^{-1} +22 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-2 z^4+1 }[/math] |
| Determinant | 225 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-a^2 z^4+z^4 a^{-4} -3 z^4+a^4 z^2-a^2 z^2+z^2 a^{-2} -z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +7 a^2 z^{10}+10 z^{10} a^{-2} +17 z^{10}+8 a^3 z^9+11 a z^9+17 z^9 a^{-1} +14 z^9 a^{-3} +7 a^4 z^8-5 a^2 z^8-12 z^8 a^{-2} +11 z^8 a^{-4} -35 z^8+4 a^5 z^7-9 a^3 z^7-32 a z^7-54 z^7 a^{-1} -30 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-13 a^4 z^6-6 a^2 z^6-5 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} +26 z^6-9 a^5 z^5-6 a^3 z^5+26 a z^5+50 z^5 a^{-1} +19 z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+6 a^4 z^4+7 a^2 z^4+8 z^4 a^{-2} +9 z^4 a^{-4} -z^4 a^{-6} -3 z^4+6 a^5 z^3+9 a^3 z^3-2 a z^3-11 z^3 a^{-1} -5 z^3 a^{-3} +z^3 a^{-5} +a^6 z^2-a^4 z^2-4 a^2 z^2-z^2 a^{-2} -z^2 a^{-4} -2 z^2-a^5 z-3 a^3 z-3 a z-z a^{-1} +1 }[/math] |
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