K12a220
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-9 q^6+16 q^5-23 q^4+28 q^3-29 q^2+27 q-22+15 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-22 t^2+40 t-47+40 t^{-1} -22 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-z^2+1 }[/math] |
| Determinant | 187 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-12 z^4 a^{-2} +7 z^4 a^{-4} -z^4 a^{-6} +7 z^4-2 a^2 z^2-14 z^2 a^{-2} +9 z^2 a^{-4} -2 z^2 a^{-6} +8 z^2-5 a^{-2} +4 a^{-4} - a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +9 z^{10} a^{-2} +5 z^{10} a^{-4} +4 z^{10}+6 a z^9+16 z^9 a^{-1} +20 z^9 a^{-3} +10 z^9 a^{-5} +4 a^2 z^8-3 z^8 a^{-2} +11 z^8 a^{-4} +11 z^8 a^{-6} +z^8+a^3 z^7-18 a z^7-54 z^7 a^{-1} -54 z^7 a^{-3} -11 z^7 a^{-5} +8 z^7 a^{-7} -14 a^2 z^6-45 z^6 a^{-2} -47 z^6 a^{-4} -17 z^6 a^{-6} +4 z^6 a^{-8} -33 z^6-3 a^3 z^5+16 a z^5+56 z^5 a^{-1} +49 z^5 a^{-3} -11 z^5 a^{-7} +z^5 a^{-9} +15 a^2 z^4+66 z^4 a^{-2} +53 z^4 a^{-4} +12 z^4 a^{-6} -5 z^4 a^{-8} +45 z^4+2 a^3 z^3-6 a z^3-26 z^3 a^{-1} -19 z^3 a^{-3} +5 z^3 a^{-5} +5 z^3 a^{-7} -z^3 a^{-9} -5 a^2 z^2-34 z^2 a^{-2} -24 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} -21 z^2+a z+4 z a^{-1} +3 z a^{-3} -z a^{-5} -z a^{-7} +5 a^{-2} +4 a^{-4} + a^{-6} +3 }[/math] |
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