K12n40
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+3 q^5-5 q^4+8 q^3-10 q^2+10 q-9+8 q^{-1} -5 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-10 t^2+11 t-9+11 t^{-1} -10 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6+1 }[/math] |
| Determinant | 63 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-13 z^4 a^{-2} +5 z^4 a^{-4} +9 z^4-3 a^2 z^2-14 z^2 a^{-2} +7 z^2 a^{-4} -z^2 a^{-6} +11 z^2-a^2-6 a^{-2} +4 a^{-4} - a^{-6} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+3 a z^9+6 z^9 a^{-1} +3 z^9 a^{-3} +3 a^2 z^8+4 z^8 a^{-2} +3 z^8 a^{-4} +4 z^8+a^3 z^7-10 a z^7-22 z^7 a^{-1} -10 z^7 a^{-3} +z^7 a^{-5} -13 a^2 z^6-30 z^6 a^{-2} -12 z^6 a^{-4} -31 z^6-4 a^3 z^5+4 a z^5+19 z^5 a^{-1} +10 z^5 a^{-3} -z^5 a^{-5} +16 a^2 z^4+49 z^4 a^{-2} +23 z^4 a^{-4} +3 z^4 a^{-6} +45 z^4+4 a^3 z^3+4 a z^3-2 z^3 a^{-1} +3 z^3 a^{-5} +z^3 a^{-7} -8 a^2 z^2-30 z^2 a^{-2} -17 z^2 a^{-4} -4 z^2 a^{-6} -25 z^2-a^3 z-2 a z-z a^{-1} -z a^{-3} -2 z a^{-5} -z a^{-7} +a^2+6 a^{-2} +4 a^{-4} + a^{-6} +5 }[/math] |
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