K12a825
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-7 q^3+12 q^2-17 q+21-21 q^{-1} +20 q^{-2} -15 q^{-3} +11 q^{-4} -6 q^{-5} +2 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-7 t^3+16 t^2-27 t+33-27 t^{-1} +16 t^{-2} -7 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+9 z^6+14 z^4+6 z^2+1 }[/math] |
| Determinant | 137 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+6 a^2 z^6-z^6 a^{-2} +5 z^6-5 a^4 z^4+15 a^2 z^4-4 z^4 a^{-2} +8 z^4-9 a^4 z^2+18 a^2 z^2-5 z^2 a^{-2} +2 z^2-5 a^4+9 a^2- a^{-2} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+7 a^2 z^{10}+4 z^{10}+3 a^5 z^9+5 a^3 z^9+9 a z^9+7 z^9 a^{-1} +2 a^6 z^8-9 a^4 z^8-22 a^2 z^8+8 z^8 a^{-2} -3 z^8+a^7 z^7-9 a^5 z^7-24 a^3 z^7-35 a z^7-15 z^7 a^{-1} +6 z^7 a^{-3} -7 a^6 z^6+17 a^4 z^6+41 a^2 z^6-20 z^6 a^{-2} +3 z^6 a^{-4} -6 z^6-5 a^7 z^5+7 a^5 z^5+41 a^3 z^5+57 a z^5+14 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} +6 a^6 z^4-31 a^4 z^4-53 a^2 z^4+23 z^4 a^{-2} -5 z^4 a^{-4} +12 z^4+8 a^7 z^3-2 a^5 z^3-42 a^3 z^3-44 a z^3+10 z^3 a^{-3} -2 z^3 a^{-5} +23 a^4 z^2+32 a^2 z^2-9 z^2 a^{-2} -4 a^7 z+a^5 z+14 a^3 z+12 a z-3 z a^{-3} -5 a^4-9 a^2+ a^{-2} -2 }[/math] |
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