K13a343
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Polynomial invariants
| Jones polynomial | Data:K13a343/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+37 t^2-68 t+83-68 t^{-1} +37 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a343/Conway Polynomial |
| Determinant | 321 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+4 a^2 z^6-2 z^6 a^{-2} +3 z^6-3 a^4 z^4+9 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +4 z^4-5 a^4 z^2+12 a^2 z^2-7 z^2 a^{-2} +2 z^2 a^{-4} +2 z^2-4 a^4+7 a^2-3 a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{12}+z^{12}+5 a^3 z^{11}+9 a z^{11}+4 z^{11} a^{-1} +10 a^4 z^{10}+23 a^2 z^{10}+8 z^{10} a^{-2} +21 z^{10}+9 a^5 z^9+16 a^3 z^9+20 a z^9+23 z^9 a^{-1} +10 z^9 a^{-3} +4 a^6 z^8-17 a^4 z^8-44 a^2 z^8+8 z^8 a^{-2} +8 z^8 a^{-4} -23 z^8+a^7 z^7-24 a^5 z^7-72 a^3 z^7-92 a z^7-59 z^7 a^{-1} -10 z^7 a^{-3} +4 z^7 a^{-5} -10 a^6 z^6+a^4 z^6+6 a^2 z^6-42 z^6 a^{-2} -14 z^6 a^{-4} +z^6 a^{-6} -32 z^6-3 a^7 z^5+25 a^5 z^5+88 a^3 z^5+103 a z^5+47 z^5 a^{-1} -4 z^5 a^{-3} -8 z^5 a^{-5} +8 a^6 z^4+4 a^4 z^4+16 a^2 z^4+45 z^4 a^{-2} +10 z^4 a^{-4} -2 z^4 a^{-6} +53 z^4+3 a^7 z^3-17 a^5 z^3-58 a^3 z^3-58 a z^3-16 z^3 a^{-1} +10 z^3 a^{-3} +6 z^3 a^{-5} -2 a^6 z^2+4 a^4 z^2+a^2 z^2-19 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-6} -19 z^2-a^7 z+7 a^5 z+19 a^3 z+17 a z+4 z a^{-1} -4 z a^{-3} -2 z a^{-5} -4 a^4-7 a^2+3 a^{-2} + a^{-4} }[/math] |
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