K12a798
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+11 q^{10}-19 q^9+26 q^8-33 q^7+34 q^6-31 q^5+25 q^4-16 q^3+9 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+23 t^2-48 t+61-48 t^{-1} +23 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-7 z^4-z^2+1 }[/math] |
| Determinant | 213 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -9 z^4 a^{-6} +z^4 a^{-10} +2 z^2 a^{-2} +4 z^2 a^{-4} -10 z^2 a^{-6} +2 z^2 a^{-8} +z^2 a^{-10} + a^{-2} +3 a^{-4} -4 a^{-6} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +5 z^{10} a^{-6} +12 z^{10} a^{-8} +7 z^{10} a^{-10} +7 z^9 a^{-5} +12 z^9 a^{-7} +16 z^9 a^{-9} +11 z^9 a^{-11} +6 z^8 a^{-4} +5 z^8 a^{-6} -10 z^8 a^{-8} +9 z^8 a^{-12} +3 z^7 a^{-3} -8 z^7 a^{-5} -19 z^7 a^{-7} -33 z^7 a^{-9} -21 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -12 z^6 a^{-4} -27 z^6 a^{-6} -13 z^6 a^{-8} -19 z^6 a^{-10} -19 z^6 a^{-12} +z^6 a^{-14} -6 z^5 a^{-3} -2 z^5 a^{-5} -7 z^5 a^{-7} +12 z^5 a^{-9} +16 z^5 a^{-11} -7 z^5 a^{-13} -3 z^4 a^{-2} +11 z^4 a^{-4} +32 z^4 a^{-6} +15 z^4 a^{-8} +14 z^4 a^{-10} +15 z^4 a^{-12} -2 z^4 a^{-14} +3 z^3 a^{-3} +8 z^3 a^{-5} +23 z^3 a^{-7} +4 z^3 a^{-9} -11 z^3 a^{-11} +3 z^3 a^{-13} +3 z^2 a^{-2} -8 z^2 a^{-4} -18 z^2 a^{-6} -2 z^2 a^{-8} -3 z^2 a^{-10} -7 z^2 a^{-12} +z^2 a^{-14} -6 z a^{-5} -9 z a^{-7} +z a^{-9} +4 z a^{-11} - a^{-2} +3 a^{-4} +4 a^{-6} - a^{-10} }[/math] |
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