K12a603
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-11 q^6+19 q^5-27 q^4+32 q^3-34 q^2+31 q-24+17 q^{-1} -9 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-22 t^2+50 t-63+50 t^{-1} -22 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+2 z^4-2 z^2+1 }[/math] |
| Determinant | 215 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+3 z^4 a^{-2} -z^4 a^{-6} +z^4-a^2 z^2-2 z^2 a^{-4} +z^2- a^{-2} - a^{-4} + a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +17 z^{10} a^{-2} +10 z^{10} a^{-4} +7 z^{10}+7 a z^9+9 z^9 a^{-1} +17 z^9 a^{-3} +15 z^9 a^{-5} +4 a^2 z^8-42 z^8 a^{-2} -8 z^8 a^{-4} +15 z^8 a^{-6} -15 z^8+a^3 z^7-21 a z^7-47 z^7 a^{-1} -57 z^7 a^{-3} -21 z^7 a^{-5} +11 z^7 a^{-7} -13 a^2 z^6+30 z^6 a^{-2} -8 z^6 a^{-4} -19 z^6 a^{-6} +5 z^6 a^{-8} +z^6-3 a^3 z^5+18 a z^5+54 z^5 a^{-1} +52 z^5 a^{-3} +5 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +12 a^2 z^4-2 z^4 a^{-2} +4 z^4 a^{-4} +z^4 a^{-6} -4 z^4 a^{-8} +11 z^4+2 a^3 z^3-7 a z^3-21 z^3 a^{-1} -10 z^3 a^{-3} +4 z^3 a^{-5} +2 z^3 a^{-7} -4 a^2 z^2-3 z^2 a^{-2} +5 z^2 a^{-4} +4 z^2 a^{-6} -8 z^2+a z+z a^{-1} -3 z a^{-3} -3 z a^{-5} + a^{-2} - a^{-4} - a^{-6} +2 }[/math] |
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