K13a1002
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Polynomial invariants
| Jones polynomial | Data:K13a1002/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+26 t^2-42 t+49-42 t^{-1} +26 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1002/Conway Polynomial |
| Determinant | 209 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8 a^{-4} +5 z^6 a^{-2} +4 z^6 a^{-4} -2 z^6 a^{-6} -z^6+10 z^4 a^{-2} +6 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} -4 z^4+10 z^2 a^{-2} +5 z^2 a^{-4} -8 z^2 a^{-6} +2 z^2 a^{-8} -5 z^2+4 a^{-2} +2 a^{-4} -4 a^{-6} + a^{-8} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-2} +z^{12} a^{-4} +3 z^{11} a^{-1} +8 z^{11} a^{-3} +5 z^{11} a^{-5} +8 z^{10} a^{-2} +16 z^{10} a^{-4} +11 z^{10} a^{-6} +3 z^{10}+a z^9-10 z^9 a^{-1} -20 z^9 a^{-3} +7 z^9 a^{-5} +16 z^9 a^{-7} -55 z^8 a^{-2} -67 z^8 a^{-4} -11 z^8 a^{-6} +18 z^8 a^{-8} -17 z^8-6 a z^7-3 z^7 a^{-1} -18 z^7 a^{-3} -60 z^7 a^{-5} -24 z^7 a^{-7} +15 z^7 a^{-9} +98 z^6 a^{-2} +71 z^6 a^{-4} -32 z^6 a^{-6} -30 z^6 a^{-8} +9 z^6 a^{-10} +34 z^6+13 a z^5+38 z^5 a^{-1} +72 z^5 a^{-3} +62 z^5 a^{-5} -9 z^5 a^{-7} -20 z^5 a^{-9} +4 z^5 a^{-11} -67 z^4 a^{-2} -21 z^4 a^{-4} +38 z^4 a^{-6} +14 z^4 a^{-8} -6 z^4 a^{-10} +z^4 a^{-12} -29 z^4-12 a z^3-38 z^3 a^{-1} -50 z^3 a^{-3} -17 z^3 a^{-5} +18 z^3 a^{-7} +10 z^3 a^{-9} -z^3 a^{-11} +21 z^2 a^{-2} -z^2 a^{-4} -16 z^2 a^{-6} -4 z^2 a^{-8} +z^2 a^{-10} +11 z^2+4 a z+11 z a^{-1} +11 z a^{-3} -z a^{-5} -7 z a^{-7} -2 z a^{-9} -4 a^{-2} +2 a^{-4} +4 a^{-6} + a^{-8} -2 }[/math] |
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