K12a804
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+5 q^{10}-13 q^9+23 q^8-32 q^7+38 q^6-40 q^5+36 q^4-28 q^3+19 q^2-9 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+32 t^2-50 t+57-50 t^{-1} +32 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+4 z^6+2 z^2+1 }[/math] |
| Determinant | 249 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +4 z^6 a^{-4} +2 z^6 a^{-6} -z^6 a^{-8} -3 z^4 a^{-2} +8 z^4 a^{-4} -4 z^4 a^{-6} -z^4 a^{-8} -2 z^2 a^{-2} +11 z^2 a^{-4} -11 z^2 a^{-6} +4 z^2 a^{-8} +5 a^{-4} -7 a^{-6} +4 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-5} +3 z^{11} a^{-7} +7 z^{10} a^{-4} +19 z^{10} a^{-6} +12 z^{10} a^{-8} +7 z^9 a^{-3} +15 z^9 a^{-5} +29 z^9 a^{-7} +21 z^9 a^{-9} +4 z^8 a^{-2} -9 z^8 a^{-4} -30 z^8 a^{-6} +4 z^8 a^{-8} +21 z^8 a^{-10} +z^7 a^{-1} -19 z^7 a^{-3} -58 z^7 a^{-5} -80 z^7 a^{-7} -29 z^7 a^{-9} +13 z^7 a^{-11} -13 z^6 a^{-2} -16 z^6 a^{-4} -15 z^6 a^{-6} -48 z^6 a^{-8} -31 z^6 a^{-10} +5 z^6 a^{-12} -3 z^5 a^{-1} +16 z^5 a^{-3} +60 z^5 a^{-5} +62 z^5 a^{-7} +7 z^5 a^{-9} -13 z^5 a^{-11} +z^5 a^{-13} +14 z^4 a^{-2} +36 z^4 a^{-4} +49 z^4 a^{-6} +45 z^4 a^{-8} +16 z^4 a^{-10} -2 z^4 a^{-12} +2 z^3 a^{-1} -6 z^3 a^{-3} -23 z^3 a^{-5} -17 z^3 a^{-7} +2 z^3 a^{-9} +4 z^3 a^{-11} -6 z^2 a^{-2} -24 z^2 a^{-4} -32 z^2 a^{-6} -19 z^2 a^{-8} -5 z^2 a^{-10} +2 z a^{-3} +3 z a^{-5} +z a^{-7} -z a^{-9} -z a^{-11} +5 a^{-4} +7 a^{-6} +4 a^{-8} + a^{-10} }[/math] |
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