K13a1862
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Polynomial invariants
| Jones polynomial | Data:K13a1862/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-6 t^4+20 t^3-44 t^2+70 t-81+70 t^{-1} -44 t^{-2} +20 t^{-3} -6 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K13a1862/Conway Polynomial |
| Determinant | 363 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +7 z^8 a^{-2} -2 z^8 a^{-4} -z^8+21 z^6 a^{-2} -10 z^6 a^{-4} +z^6 a^{-6} -5 z^6+32 z^4 a^{-2} -19 z^4 a^{-4} +3 z^4 a^{-6} -10 z^4+25 z^2 a^{-2} -16 z^2 a^{-4} +3 z^2 a^{-6} -9 z^2+9 a^{-2} -6 a^{-4} + a^{-6} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +7 z^{11} a^{-1} +16 z^{11} a^{-3} +9 z^{11} a^{-5} +25 z^{10} a^{-2} +32 z^{10} a^{-4} +17 z^{10} a^{-6} +10 z^{10}+8 a z^9+4 z^9 a^{-1} -7 z^9 a^{-3} +15 z^9 a^{-5} +18 z^9 a^{-7} +4 a^2 z^8-68 z^8 a^{-2} -79 z^8 a^{-4} -21 z^8 a^{-6} +12 z^8 a^{-8} -18 z^8+a^3 z^7-19 a z^7-37 z^7 a^{-1} -45 z^7 a^{-3} -65 z^7 a^{-5} -32 z^7 a^{-7} +5 z^7 a^{-9} -11 a^2 z^6+72 z^6 a^{-2} +76 z^6 a^{-4} +2 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} +8 z^6-3 a^3 z^5+14 a z^5+39 z^5 a^{-1} +61 z^5 a^{-3} +67 z^5 a^{-5} +21 z^5 a^{-7} -7 z^5 a^{-9} +10 a^2 z^4-56 z^4 a^{-2} -49 z^4 a^{-4} +3 z^4 a^{-6} +10 z^4 a^{-8} -z^4 a^{-10} -5 z^4+3 a^3 z^3-3 a z^3-19 z^3 a^{-1} -36 z^3 a^{-3} -31 z^3 a^{-5} -6 z^3 a^{-7} +2 z^3 a^{-9} -3 a^2 z^2+31 z^2 a^{-2} +23 z^2 a^{-4} +2 z^2 a^{-6} -z^2 a^{-8} +8 z^2-a^3 z+5 z a^{-1} +10 z a^{-3} +7 z a^{-5} +z a^{-7} -9 a^{-2} -6 a^{-4} - a^{-6} -3 }[/math] |
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