K12n810
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-6 q^2+8 q-9+9 q^{-1} -8 q^{-2} +6 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-8 t^2+12 t-11+12 t^{-1} -8 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+4 z^4-2 z^2+1 }[/math] |
| Determinant | 55 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6-3 a^2 z^4-2 z^4 a^{-2} +9 z^4+a^4 z^2-9 a^2 z^2-6 z^2 a^{-2} +12 z^2+2 a^4-5 a^2-3 a^{-2} + a^{-4} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{10}+2 z^{10}+3 a^3 z^9+9 a z^9+6 z^9 a^{-1} +a^4 z^8-4 a^2 z^8+5 z^8 a^{-2} -15 a^3 z^7-44 a z^7-28 z^7 a^{-1} +z^7 a^{-3} -5 a^4 z^6-16 a^2 z^6-23 z^6 a^{-2} -34 z^6+23 a^3 z^5+62 a z^5+36 z^5 a^{-1} -3 z^5 a^{-3} +9 a^4 z^4+40 a^2 z^4+29 z^4 a^{-2} +60 z^4-13 a^3 z^3-31 a z^3-18 z^3 a^{-1} -7 a^4 z^2-26 a^2 z^2-15 z^2 a^{-2} -z^2 a^{-4} -33 z^2+3 a^3 z+5 a z+3 z a^{-1} +z a^{-3} +2 a^4+5 a^2+3 a^{-2} + a^{-4} +6 }[/math] |
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