K12n513
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-5 q^{11}+10 q^{10}-15 q^9+19 q^8-21 q^7+20 q^6-16 q^5+11 q^4-5 q^3+2 q^2 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-29 t+37-29 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4+5 z^2+1 }[/math] |
| Determinant | 125 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-6} -z^6 a^{-8} +2 z^4 a^{-4} -z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +4 z^2 a^{-4} +z^2 a^{-8} +2 a^{-4} - a^{-6} + a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-8} +2 z^{10} a^{-10} +4 z^9 a^{-7} +11 z^9 a^{-9} +7 z^9 a^{-11} +3 z^8 a^{-6} +6 z^8 a^{-8} +12 z^8 a^{-10} +9 z^8 a^{-12} +z^7 a^{-5} -5 z^7 a^{-7} -20 z^7 a^{-9} -9 z^7 a^{-11} +5 z^7 a^{-13} -2 z^6 a^{-6} -17 z^6 a^{-8} -37 z^6 a^{-10} -21 z^6 a^{-12} +z^6 a^{-14} +3 z^5 a^{-5} +10 z^5 a^{-7} +9 z^5 a^{-9} -8 z^5 a^{-11} -10 z^5 a^{-13} +3 z^4 a^{-4} +6 z^4 a^{-6} +18 z^4 a^{-8} +26 z^4 a^{-10} +10 z^4 a^{-12} -z^4 a^{-14} -3 z^3 a^{-5} -7 z^3 a^{-7} +7 z^3 a^{-11} +3 z^3 a^{-13} -5 z^2 a^{-4} -5 z^2 a^{-6} -7 z^2 a^{-8} -7 z^2 a^{-10} +2 z a^{-7} -z a^{-11} +z a^{-13} +2 a^{-4} + a^{-6} + a^{-8} + a^{-10} }[/math] |
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