K12a1222
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-17 q^3+25 q^2-30 q+33-30 q^{-1} +25 q^{-2} -17 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+5 t^4-13 t^3+25 t^2-37 t+43-37 t^{-1} +25 t^{-2} -13 t^{-3} +5 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-5 z^8-8 z^6-3 z^4+z^2+1 }[/math] |
| Determinant | 205 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -7 z^8+5 a^2 z^6+5 z^6 a^{-2} -18 z^6+8 a^2 z^4+8 z^4 a^{-2} -19 z^4+3 a^2 z^2+3 z^2 a^{-2} -5 z^2-a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +7 a^2 z^{10}+8 z^{10} a^{-2} +15 z^{10}+8 a^3 z^9+6 a z^9+8 z^9 a^{-1} +10 z^9 a^{-3} +7 a^4 z^8-9 a^2 z^8-14 z^8 a^{-2} +8 z^8 a^{-4} -38 z^8+4 a^5 z^7-10 a^3 z^7-16 a z^7-29 z^7 a^{-1} -23 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-13 a^4 z^6+8 a^2 z^6+11 z^6 a^{-2} -19 z^6 a^{-4} +z^6 a^{-6} +53 z^6-9 a^5 z^5-5 a^3 z^5+11 a z^5+35 z^5 a^{-1} +19 z^5 a^{-3} -9 z^5 a^{-5} -2 a^6 z^4+5 a^4 z^4-12 a^2 z^4-5 z^4 a^{-2} +13 z^4 a^{-4} -2 z^4 a^{-6} -39 z^4+6 a^5 z^3+10 a^3 z^3-3 a z^3-16 z^3 a^{-1} -5 z^3 a^{-3} +4 z^3 a^{-5} +a^6 z^2+a^4 z^2+4 a^2 z^2+z^2 a^{-2} -2 z^2 a^{-4} +7 z^2-a^5 z-3 a^3 z-2 a z+a^2+ a^{-2} +3 }[/math] |
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