K12a625
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+17 q^2-25 q+31-33 q^{-1} +31 q^{-2} -25 q^{-3} +18 q^{-4} -10 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+19 t^2-49 t+67-49 t^{-1} +19 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+z^4+1 }[/math] |
| Determinant | 209 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+3 z^4 a^4+5 z^2 a^4+3 a^4-2 z^6 a^2-5 z^4 a^2-7 z^2 a^2-3 a^2-z^6+z^4+3 z^2+2+2 z^4 a^{-2} +z^2 a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+14 a^2 z^{10}+8 z^{10}+7 a^5 z^9+16 a^3 z^9+22 a z^9+13 z^9 a^{-1} +4 a^6 z^8-5 a^4 z^8-21 a^2 z^8+12 z^8 a^{-2} +a^7 z^7-18 a^5 z^7-57 a^3 z^7-69 a z^7-23 z^7 a^{-1} +8 z^7 a^{-3} -12 a^6 z^6-22 a^4 z^6-16 a^2 z^6-19 z^6 a^{-2} +4 z^6 a^{-4} -29 z^6-3 a^7 z^5+11 a^5 z^5+54 a^3 z^5+71 a z^5+20 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +12 a^6 z^4+29 a^4 z^4+36 a^2 z^4+13 z^4 a^{-2} -5 z^4 a^{-4} +37 z^4+3 a^7 z^3-a^5 z^3-23 a^3 z^3-30 a z^3-7 z^3 a^{-1} +3 z^3 a^{-3} -z^3 a^{-5} -5 a^6 z^2-14 a^4 z^2-19 a^2 z^2-3 z^2 a^{-2} +z^2 a^{-4} -14 z^2-a^7 z+4 a^3 z+4 a z+z a^{-1} +a^6+3 a^4+3 a^2+2 }[/math] |
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