K12a475
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-13 q^6+23 q^5-32 q^4+39 q^3-41 q^2+37 q-29+20 q^{-1} -10 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-28 t^2+56 t-69+56 t^{-1} -28 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-z^8 }[/math] |
| Determinant | 255 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-9 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +6 z^4-2 a^2 z^2-11 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +8 z^2-a^2-6 a^{-2} +4 a^{-4} - a^{-6} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +19 z^{10} a^{-2} +12 z^{10} a^{-4} +7 z^{10}+7 a z^9+16 z^9 a^{-1} +30 z^9 a^{-3} +21 z^9 a^{-5} +4 a^2 z^8-25 z^8 a^{-2} +6 z^8 a^{-4} +21 z^8 a^{-6} -6 z^8+a^3 z^7-16 a z^7-53 z^7 a^{-1} -77 z^7 a^{-3} -28 z^7 a^{-5} +13 z^7 a^{-7} -12 a^2 z^6-24 z^6 a^{-2} -51 z^6 a^{-4} -31 z^6 a^{-6} +5 z^6 a^{-8} -21 z^6-3 a^3 z^5+8 a z^5+40 z^5 a^{-1} +49 z^5 a^{-3} +6 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4+47 z^4 a^{-2} +45 z^4 a^{-4} +17 z^4 a^{-6} -2 z^4 a^{-8} +34 z^4+3 a^3 z^3+3 a z^3-6 z^3 a^{-1} -6 z^3 a^{-3} +4 z^3 a^{-5} +4 z^3 a^{-7} -6 a^2 z^2-27 z^2 a^{-2} -18 z^2 a^{-4} -5 z^2 a^{-6} -20 z^2-a^3 z-2 a z-z a^{-1} -z a^{-3} -2 z a^{-5} -z a^{-7} +a^2+6 a^{-2} +4 a^{-4} + a^{-6} +5 }[/math] |
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