K13a1131
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Polynomial invariants
| Jones polynomial | Data:K13a1131/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-7 t^4+23 t^3-48 t^2+73 t-83+73 t^{-1} -48 t^{-2} +23 t^{-3} -7 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K13a1131/Conway Polynomial |
| Determinant | 387 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +6 z^8 a^{-2} -2 z^8 a^{-4} -z^8+14 z^6 a^{-2} -9 z^6 a^{-4} +z^6 a^{-6} -4 z^6+15 z^4 a^{-2} -13 z^4 a^{-4} +3 z^4 a^{-6} -5 z^4+7 z^2 a^{-2} -6 z^2 a^{-4} +2 z^2 a^{-6} -2 z^2+2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-2} +3 z^{12} a^{-4} +10 z^{11} a^{-1} +22 z^{11} a^{-3} +12 z^{11} a^{-5} +30 z^{10} a^{-2} +36 z^{10} a^{-4} +20 z^{10} a^{-6} +14 z^{10}+11 a z^9-z^9 a^{-1} -27 z^9 a^{-3} +4 z^9 a^{-5} +19 z^9 a^{-7} +5 a^2 z^8-97 z^8 a^{-2} -111 z^8 a^{-4} -36 z^8 a^{-6} +12 z^8 a^{-8} -29 z^8+a^3 z^7-27 a z^7-45 z^7 a^{-1} -35 z^7 a^{-3} -60 z^7 a^{-5} -37 z^7 a^{-7} +5 z^7 a^{-9} -12 a^2 z^6+105 z^6 a^{-2} +123 z^6 a^{-4} +24 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} +15 z^6-2 a^3 z^5+20 a z^5+54 z^5 a^{-1} +77 z^5 a^{-3} +79 z^5 a^{-5} +27 z^5 a^{-7} -7 z^5 a^{-9} +8 a^2 z^4-55 z^4 a^{-2} -58 z^4 a^{-4} -7 z^4 a^{-6} +8 z^4 a^{-8} -z^4 a^{-10} -5 z^4+a^3 z^3-6 a z^3-26 z^3 a^{-1} -42 z^3 a^{-3} -34 z^3 a^{-5} -10 z^3 a^{-7} +z^3 a^{-9} -a^2 z^2+12 z^2 a^{-2} +12 z^2 a^{-4} +2 z^2 a^{-6} -z^2 a^{-8} +2 z^2+a z+4 z a^{-1} +7 z a^{-3} +5 z a^{-5} +z a^{-7} -2 a^{-2} - a^{-4} }[/math] |
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