K12a653
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{14}-4 q^{13}+8 q^{12}-13 q^{11}+17 q^{10}-21 q^9+22 q^8-20 q^7+17 q^6-11 q^5+7 q^4-3 q^3+q^2 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 11 t^2-36 t+51-36 t^{-1} +11 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 11 z^4+8 z^2+1 }[/math] |
| Determinant | 145 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^{-4} +3 z^4 a^{-6} +4 z^4 a^{-8} +3 z^4 a^{-10} +z^2 a^{-4} +4 z^2 a^{-6} +4 z^2 a^{-8} +3 z^2 a^{-10} -4 z^2 a^{-12} +2 a^{-6} + a^{-10} -3 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-11} +2 z^{11} a^{-13} +6 z^{10} a^{-10} +11 z^{10} a^{-12} +5 z^{10} a^{-14} +8 z^9 a^{-9} +8 z^9 a^{-11} +4 z^9 a^{-13} +4 z^9 a^{-15} +9 z^8 a^{-8} -9 z^8 a^{-10} -38 z^8 a^{-12} -19 z^8 a^{-14} +z^8 a^{-16} +8 z^7 a^{-7} -10 z^7 a^{-9} -43 z^7 a^{-11} -43 z^7 a^{-13} -18 z^7 a^{-15} +6 z^6 a^{-6} -12 z^6 a^{-8} -3 z^6 a^{-10} +35 z^6 a^{-12} +16 z^6 a^{-14} -4 z^6 a^{-16} +3 z^5 a^{-5} -9 z^5 a^{-7} -8 z^5 a^{-9} +47 z^5 a^{-11} +68 z^5 a^{-13} +25 z^5 a^{-15} +z^4 a^{-4} -7 z^4 a^{-6} +2 z^4 a^{-8} -2 z^4 a^{-10} -13 z^4 a^{-12} +4 z^4 a^{-14} +5 z^4 a^{-16} -2 z^3 a^{-5} +4 z^3 a^{-7} +11 z^3 a^{-9} -20 z^3 a^{-11} -37 z^3 a^{-13} -12 z^3 a^{-15} -z^2 a^{-4} +6 z^2 a^{-6} +2 z^2 a^{-8} +4 z^2 a^{-10} +8 z^2 a^{-12} -3 z^2 a^{-14} -2 z^2 a^{-16} -4 z a^{-9} +2 z a^{-11} +8 z a^{-13} +2 z a^{-15} -2 a^{-6} - a^{-10} -3 a^{-12} - a^{-14} }[/math] |
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