K12a34
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-4 q^{12}+7 q^{11}-11 q^{10}+15 q^9-17 q^8+17 q^7-15 q^6+12 q^5-8 q^4+5 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-16 t^2+20 t-21+20 t^{-1} -16 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-2 z^4+5 z^2+1 }[/math] |
| Determinant | 115 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -5 z^6 a^{-6} -4 z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-4} -8 z^4 a^{-6} -2 z^4 a^{-8} +3 z^4 a^{-10} +7 z^2 a^{-4} -7 z^2 a^{-6} +5 z^2 a^{-8} +3 a^{-4} -4 a^{-6} +4 a^{-8} -2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +6 z^{10} a^{-8} +4 z^{10} a^{-10} +2 z^9 a^{-5} +2 z^9 a^{-7} +7 z^9 a^{-9} +7 z^9 a^{-11} +z^8 a^{-4} -6 z^8 a^{-6} -20 z^8 a^{-8} -5 z^8 a^{-10} +8 z^8 a^{-12} -10 z^7 a^{-5} -23 z^7 a^{-7} -35 z^7 a^{-9} -14 z^7 a^{-11} +8 z^7 a^{-13} -6 z^6 a^{-4} -4 z^6 a^{-6} +10 z^6 a^{-8} -9 z^6 a^{-10} -10 z^6 a^{-12} +7 z^6 a^{-14} +15 z^5 a^{-5} +37 z^5 a^{-7} +42 z^5 a^{-9} +9 z^5 a^{-11} -7 z^5 a^{-13} +4 z^5 a^{-15} +12 z^4 a^{-4} +21 z^4 a^{-6} +16 z^4 a^{-8} +14 z^4 a^{-10} -z^4 a^{-12} -7 z^4 a^{-14} +z^4 a^{-16} -8 z^3 a^{-5} -21 z^3 a^{-7} -17 z^3 a^{-9} -4 z^3 a^{-11} -3 z^3 a^{-13} -3 z^3 a^{-15} -10 z^2 a^{-4} -17 z^2 a^{-6} -16 z^2 a^{-8} -7 z^2 a^{-10} +3 z^2 a^{-12} +z^2 a^{-14} +z a^{-5} +4 z a^{-7} +2 z a^{-9} +z a^{-11} +2 z a^{-13} +3 a^{-4} +4 a^{-6} +4 a^{-8} +2 a^{-10} }[/math] |
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