K12n576
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^{13}+3 q^{12}-4 q^{11}+5 q^{10}-5 q^9+5 q^8-4 q^7+3 q^6-q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-4 t^3+5 t^2-4 t+3-4 t^{-1} +5 t^{-2} -4 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+12 z^6+21 z^4+12 z^2+1 }[/math] |
| Determinant | 33 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +z^8 a^{-10} +7 z^6 a^{-8} +6 z^6 a^{-10} -z^6 a^{-12} +16 z^4 a^{-8} +11 z^4 a^{-10} -6 z^4 a^{-12} +13 z^2 a^{-8} +8 z^2 a^{-10} -10 z^2 a^{-12} +z^2 a^{-14} +2 a^{-8} +3 a^{-10} -5 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-9} +3 z^9 a^{-11} +2 z^9 a^{-13} +z^8 a^{-8} -5 z^8 a^{-10} -4 z^8 a^{-12} +2 z^8 a^{-14} -5 z^7 a^{-9} -15 z^7 a^{-11} -9 z^7 a^{-13} +z^7 a^{-15} -7 z^6 a^{-8} +8 z^6 a^{-10} +7 z^6 a^{-12} -8 z^6 a^{-14} +6 z^5 a^{-9} +22 z^5 a^{-11} +13 z^5 a^{-13} -3 z^5 a^{-15} +16 z^4 a^{-8} -9 z^4 a^{-10} -17 z^4 a^{-12} +9 z^4 a^{-14} +z^4 a^{-16} -14 z^3 a^{-11} -11 z^3 a^{-13} +3 z^3 a^{-15} -13 z^2 a^{-8} +9 z^2 a^{-10} +18 z^2 a^{-12} -4 z^2 a^{-14} -z a^{-9} +5 z a^{-11} +3 z a^{-13} -z a^{-15} +2 z a^{-17} +2 a^{-8} -3 a^{-10} -5 a^{-12} - a^{-14} }[/math] |
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