K12a231
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-17 q^9+25 q^8-31 q^7+34 q^6-32 q^5+26 q^4-18 q^3+11 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+24 t^2-48 t+59-48 t^{-1} +24 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-6 z^4+3 z^2+1 }[/math] |
| Determinant | 213 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} +z^4 a^{-4} -9 z^4 a^{-6} +z^4 a^{-10} +z^2 a^{-2} +7 z^2 a^{-4} -10 z^2 a^{-6} +4 z^2 a^{-8} +z^2 a^{-10} +4 a^{-4} -5 a^{-6} +3 a^{-8} - a^{-10} }[/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} +11 z^9 a^{-5} +18 z^9 a^{-7} +15 z^9 a^{-9} +8 z^9 a^{-11} +9 z^8 a^{-4} +z^8 a^{-6} -15 z^8 a^{-8} +7 z^8 a^{-12} +4 z^7 a^{-3} -22 z^7 a^{-5} -49 z^7 a^{-7} -37 z^7 a^{-9} -10 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -20 z^6 a^{-4} -33 z^6 a^{-6} -14 z^6 a^{-8} -16 z^6 a^{-10} -13 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +14 z^5 a^{-5} +40 z^5 a^{-7} +25 z^5 a^{-9} -3 z^5 a^{-11} -9 z^5 a^{-13} -2 z^4 a^{-2} +17 z^4 a^{-4} +45 z^4 a^{-6} +33 z^4 a^{-8} +15 z^4 a^{-10} +6 z^4 a^{-12} -2 z^4 a^{-14} +2 z^3 a^{-3} -4 z^3 a^{-5} -6 z^3 a^{-7} +z^3 a^{-9} +7 z^3 a^{-11} +6 z^3 a^{-13} +z^2 a^{-2} -13 z^2 a^{-4} -25 z^2 a^{-6} -16 z^2 a^{-8} -7 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} -z a^{-5} -z a^{-7} -3 z a^{-9} -4 z a^{-11} -z a^{-13} +4 a^{-4} +5 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
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