K12a345
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{14}-3 q^{13}+6 q^{12}-10 q^{11}+12 q^{10}-15 q^9+16 q^8-14 q^7+12 q^6-8 q^5+5 q^4-2 q^3+q^2 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 8 t^2-26 t+37-26 t^{-1} +8 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 8 z^4+6 z^2+1 }[/math] |
| Determinant | 105 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^{-4} +2 z^4 a^{-6} +3 z^4 a^{-8} +2 z^4 a^{-10} +2 z^2 a^{-4} +2 z^2 a^{-6} +4 z^2 a^{-8} +z^2 a^{-10} -3 z^2 a^{-12} + a^{-4} +2 a^{-8} - a^{-10} -2 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +3 z^{10} a^{-10} +6 z^{10} a^{-12} +3 z^{10} a^{-14} +4 z^9 a^{-9} +5 z^9 a^{-11} +4 z^9 a^{-13} +3 z^9 a^{-15} +5 z^8 a^{-8} -3 z^8 a^{-10} -20 z^8 a^{-12} -11 z^8 a^{-14} +z^8 a^{-16} +4 z^7 a^{-7} -4 z^7 a^{-9} -25 z^7 a^{-11} -32 z^7 a^{-13} -15 z^7 a^{-15} +3 z^6 a^{-6} -10 z^6 a^{-8} -10 z^6 a^{-10} +14 z^6 a^{-12} +6 z^6 a^{-14} -5 z^6 a^{-16} +2 z^5 a^{-5} -4 z^5 a^{-7} -10 z^5 a^{-9} +22 z^5 a^{-11} +50 z^5 a^{-13} +24 z^5 a^{-15} +z^4 a^{-4} -2 z^4 a^{-6} +12 z^4 a^{-8} +13 z^4 a^{-10} -2 z^4 a^{-12} +8 z^4 a^{-14} +8 z^4 a^{-16} -2 z^3 a^{-5} +2 z^3 a^{-7} +16 z^3 a^{-9} -3 z^3 a^{-11} -30 z^3 a^{-13} -15 z^3 a^{-15} -2 z^2 a^{-4} -8 z^2 a^{-8} -7 z^2 a^{-10} +3 z^2 a^{-12} -4 z^2 a^{-14} -4 z^2 a^{-16} -6 z a^{-9} -2 z a^{-11} +8 z a^{-13} +4 z a^{-15} + a^{-4} +2 a^{-8} + a^{-10} -2 a^{-12} - a^{-14} }[/math] |
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