K12n228
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+5 q^{10}-7 q^9+7 q^8-7 q^7+6 q^6-3 q^5+q^4+q^3-q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+3 t^3+t^2-12 t+19-12 t^{-1} + t^{-2} +3 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-5 z^6-z^4+3 z^2+1 }[/math] |
| Determinant | 37 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} +z^6 a^{-4} -7 z^6 a^{-6} +z^6 a^{-8} +6 z^4 a^{-4} -15 z^4 a^{-6} +8 z^4 a^{-8} +9 z^2 a^{-4} -15 z^2 a^{-6} +13 z^2 a^{-8} -4 z^2 a^{-10} +4 a^{-4} -6 a^{-6} +6 a^{-8} -4 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-8} +z^{10} a^{-10} +z^9 a^{-5} +2 z^9 a^{-7} +4 z^9 a^{-9} +3 z^9 a^{-11} +z^8 a^{-4} +2 z^8 a^{-6} -3 z^8 a^{-8} +4 z^8 a^{-12} -7 z^7 a^{-5} -15 z^7 a^{-7} -21 z^7 a^{-9} -10 z^7 a^{-11} +3 z^7 a^{-13} -7 z^6 a^{-4} -17 z^6 a^{-6} -11 z^6 a^{-8} -16 z^6 a^{-10} -14 z^6 a^{-12} +z^6 a^{-14} +13 z^5 a^{-5} +30 z^5 a^{-7} +31 z^5 a^{-9} +4 z^5 a^{-11} -10 z^5 a^{-13} +15 z^4 a^{-4} +37 z^4 a^{-6} +39 z^4 a^{-8} +30 z^4 a^{-10} +10 z^4 a^{-12} -3 z^4 a^{-14} -8 z^3 a^{-5} -18 z^3 a^{-7} -11 z^3 a^{-9} +5 z^3 a^{-11} +6 z^3 a^{-13} -13 z^2 a^{-4} -28 z^2 a^{-6} -28 z^2 a^{-8} -18 z^2 a^{-10} -4 z^2 a^{-12} +z^2 a^{-14} +3 z a^{-7} +z a^{-9} -4 z a^{-11} -2 z a^{-13} +4 a^{-4} +6 a^{-6} +6 a^{-8} +4 a^{-10} + a^{-12} }[/math] |
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