K13a1956
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Polynomial invariants
| Jones polynomial | Data:K13a1956/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+37 t^2-69 t+85-69 t^{-1} +37 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1956/Conway Polynomial |
| Determinant | 325 |
| 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+7 a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} +5 z^4-3 a^4 z^2+4 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +6 z^2-a^4-2 a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{12}+2 z^{12}+7 a^3 z^{11}+15 a z^{11}+8 z^{11} a^{-1} +10 a^4 z^{10}+21 a^2 z^{10}+14 z^{10} a^{-2} +25 z^{10}+8 a^5 z^9-4 a^3 z^9-19 a z^9+8 z^9 a^{-1} +15 z^9 a^{-3} +4 a^6 z^8-27 a^4 z^8-76 a^2 z^8-15 z^8 a^{-2} +11 z^8 a^{-4} -71 z^8+a^7 z^7-24 a^5 z^7-29 a^3 z^7-22 a z^7-46 z^7 a^{-1} -23 z^7 a^{-3} +5 z^7 a^{-5} -12 a^6 z^6+28 a^4 z^6+103 a^2 z^6-10 z^6 a^{-2} -19 z^6 a^{-4} +z^6 a^{-6} +73 z^6-3 a^7 z^5+24 a^5 z^5+54 a^3 z^5+60 a z^5+45 z^5 a^{-1} +4 z^5 a^{-3} -8 z^5 a^{-5} +9 a^6 z^4-20 a^4 z^4-64 a^2 z^4+17 z^4 a^{-2} +9 z^4 a^{-4} -z^4 a^{-6} -28 z^4+2 a^7 z^3-13 a^5 z^3-38 a^3 z^3-37 a z^3-12 z^3 a^{-1} +5 z^3 a^{-3} +3 z^3 a^{-5} -a^6 z^2+8 a^4 z^2+14 a^2 z^2-8 z^2 a^{-2} -2 z^2 a^{-4} -z^2+4 a^5 z+8 a^3 z+5 a z-z a^{-1} -2 z a^{-3} -a^4+2 a^{-2} +4 }[/math] |
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