K12a314
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-18 q^9+26 q^8-32 q^7+35 q^6-32 q^5+27 q^4-18 q^3+10 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+21 t^2-51 t+67-51 t^{-1} +21 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+3 z^4+6 z^2+1 }[/math] |
| Determinant | 217 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} +z^4 a^{-2} -3 z^4 a^{-6} +5 z^4 a^{-8} +z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} +8 z^2 a^{-8} -4 z^2 a^{-10} + a^{-4} +3 a^{-8} -4 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +7 z^{10} a^{-6} +13 z^{10} a^{-8} +6 z^{10} a^{-10} +10 z^9 a^{-5} +18 z^9 a^{-7} +16 z^9 a^{-9} +8 z^9 a^{-11} +8 z^8 a^{-4} -z^8 a^{-6} -13 z^8 a^{-8} +3 z^8 a^{-10} +7 z^8 a^{-12} +4 z^7 a^{-3} -18 z^7 a^{-5} -47 z^7 a^{-7} -36 z^7 a^{-9} -7 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -16 z^6 a^{-4} -19 z^6 a^{-6} -13 z^6 a^{-8} -24 z^6 a^{-10} -12 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +12 z^5 a^{-5} +43 z^5 a^{-7} +20 z^5 a^{-9} -12 z^5 a^{-11} -9 z^5 a^{-13} -2 z^4 a^{-2} +11 z^4 a^{-4} +20 z^4 a^{-6} +24 z^4 a^{-8} +24 z^4 a^{-10} +5 z^4 a^{-12} -2 z^4 a^{-14} +4 z^3 a^{-3} -6 z^3 a^{-5} -18 z^3 a^{-7} +4 z^3 a^{-9} +19 z^3 a^{-11} +7 z^3 a^{-13} +z^2 a^{-2} -5 z^2 a^{-4} -7 z^2 a^{-6} -12 z^2 a^{-8} -13 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} +z a^{-5} +3 z a^{-7} -5 z a^{-9} -9 z a^{-11} -2 z a^{-13} + a^{-4} +3 a^{-8} +4 a^{-10} + a^{-12} }[/math] |
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