K12a788
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+13 q^7-24 q^6+36 q^5-45 q^4+48 q^3-45 q^2+37 q-25+14 q^{-1} -5 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-31 t^2+67 t-85+67 t^{-1} -31 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^4-z^2+1 }[/math] |
| Determinant | 299 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +3 z^6 a^{-4} +z^6-9 z^4 a^{-2} +7 z^4 a^{-4} -3 z^4 a^{-6} +2 z^4-8 z^2 a^{-2} +6 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} +3 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-3} +4 z^{11} a^{-5} +13 z^{10} a^{-2} +26 z^{10} a^{-4} +13 z^{10} a^{-6} +18 z^9 a^{-1} +34 z^9 a^{-3} +33 z^9 a^{-5} +17 z^9 a^{-7} +z^8 a^{-2} -28 z^8 a^{-4} -4 z^8 a^{-6} +12 z^8 a^{-8} +13 z^8+5 a z^7-30 z^7 a^{-1} -86 z^7 a^{-3} -86 z^7 a^{-5} -30 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-43 z^6 a^{-2} -26 z^6 a^{-4} -29 z^6 a^{-6} -21 z^6 a^{-8} +z^6 a^{-10} -23 z^6-6 a z^5+17 z^5 a^{-1} +62 z^5 a^{-3} +66 z^5 a^{-5} +20 z^5 a^{-7} -7 z^5 a^{-9} -a^2 z^4+40 z^4 a^{-2} +36 z^4 a^{-4} +28 z^4 a^{-6} +13 z^4 a^{-8} -z^4 a^{-10} +17 z^4+2 a z^3-6 z^3 a^{-1} -19 z^3 a^{-3} -19 z^3 a^{-5} -6 z^3 a^{-7} +2 z^3 a^{-9} -15 z^2 a^{-2} -11 z^2 a^{-4} -6 z^2 a^{-6} -3 z^2 a^{-8} -7 z^2+z a^{-1} +2 z a^{-3} +2 z a^{-5} +z a^{-7} +2 a^{-2} + a^{-4} +2 }[/math] |
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