K12n816
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+5 q^2-10 q+15-18 q^{-1} +19 q^{-2} -17 q^{-3} +14 q^{-4} -9 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+11 t^2-26 t+35-26 t^{-1} +11 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-z^4+1 }[/math] |
| Determinant | 113 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+3 z^4 a^4+6 z^2 a^4+3 a^4-2 z^6 a^2-7 z^4 a^2-9 z^2 a^2-3 a^2+3 z^4+5 z^2+2-z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^4 z^{10}+3 a^2 z^{10}+6 a^5 z^9+15 a^3 z^9+9 a z^9+4 a^6 z^8+4 a^4 z^8+8 a^2 z^8+8 z^8+a^7 z^7-17 a^5 z^7-47 a^3 z^7-27 a z^7+2 z^7 a^{-1} -13 a^6 z^6-41 a^4 z^6-51 a^2 z^6-23 z^6-3 a^7 z^5+8 a^5 z^5+38 a^3 z^5+30 a z^5+3 z^5 a^{-1} +13 a^6 z^4+48 a^4 z^4+62 a^2 z^4+5 z^4 a^{-2} +32 z^4+3 a^7 z^3+2 a^5 z^3-10 a^3 z^3-12 a z^3-2 z^3 a^{-1} +z^3 a^{-3} -6 a^6 z^2-20 a^4 z^2-26 a^2 z^2-3 z^2 a^{-2} -15 z^2-a^7 z-a^5 z+a^3 z+a z+a^6+3 a^4+3 a^2+2 }[/math] |
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