K12a670
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-12 q^5+20 q^4-29 q^3+36 q^2-37 q+35-28 q^{-1} +19 q^{-2} -10 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+29 t^2-48 t+57-48 t^{-1} +29 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+3 z^4+z^2+1 }[/math] |
| Determinant | 237 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+3 z^6 a^{-2} -z^6 a^{-4} +4 z^6-3 a^2 z^4+z^4 a^{-2} -2 z^4 a^{-4} +7 z^4-3 a^2 z^2-3 z^2 a^{-2} +7 z^2-a^2- a^{-2} +3 }[/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}+14 a z^9+21 z^9 a^{-1} +17 z^9 a^{-3} +10 z^9 a^{-5} +14 a^2 z^8-28 z^8 a^{-2} -15 z^8 a^{-4} +5 z^8 a^{-6} +6 z^8+9 a^3 z^7-14 a z^7-53 z^7 a^{-1} -59 z^7 a^{-3} -28 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-21 a^2 z^6-10 z^6 a^{-2} -6 z^6 a^{-4} -13 z^6 a^{-6} -42 z^6+a^5 z^5-11 a^3 z^5-5 a z^5+26 z^5 a^{-1} +43 z^5 a^{-3} +22 z^5 a^{-5} -2 z^5 a^{-7} -4 a^4 z^4+17 a^2 z^4+24 z^4 a^{-2} +13 z^4 a^{-4} +9 z^4 a^{-6} +41 z^4-a^5 z^3+7 a^3 z^3+14 a z^3+5 z^3 a^{-1} -5 z^3 a^{-3} -3 z^3 a^{-5} +z^3 a^{-7} +a^4 z^2-6 a^2 z^2-11 z^2 a^{-2} -3 z^2 a^{-4} -z^2 a^{-6} -16 z^2-2 a^3 z-5 a z-5 z a^{-1} -2 z a^{-3} +a^2+ a^{-2} +3 }[/math] |
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