K12a340
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+12 q^7-22 q^6+31 q^5-37 q^4+40 q^3-36 q^2+29 q-19+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-21 t^2+59 t-81+59 t^{-1} -21 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-3 z^4+2 z^2+1 }[/math] |
| Determinant | 247 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -2 z^4 a^{-2} +4 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-4 z^2 a^{-2} +7 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} -2 a^{-2} +4 a^{-4} -2 a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +9 z^{10} a^{-2} +19 z^{10} a^{-4} +10 z^{10} a^{-6} +11 z^9 a^{-1} +21 z^9 a^{-3} +24 z^9 a^{-5} +14 z^9 a^{-7} -7 z^8 a^{-2} -28 z^8 a^{-4} -2 z^8 a^{-6} +11 z^8 a^{-8} +8 z^8+4 a z^7-21 z^7 a^{-1} -66 z^7 a^{-3} -69 z^7 a^{-5} -23 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-12 z^6 a^{-2} -6 z^6 a^{-4} -31 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} -15 z^6-8 a z^5+18 z^5 a^{-1} +73 z^5 a^{-3} +61 z^5 a^{-5} +6 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+22 z^4 a^{-2} +32 z^4 a^{-4} +32 z^4 a^{-6} +10 z^4 a^{-8} -z^4 a^{-10} +9 z^4+4 a z^3-11 z^3 a^{-1} -32 z^3 a^{-3} -18 z^3 a^{-5} +2 z^3 a^{-7} +3 z^3 a^{-9} +a^2 z^2-13 z^2 a^{-2} -17 z^2 a^{-4} -12 z^2 a^{-6} -3 z^2 a^{-8} -4 z^2+2 z a^{-1} +4 z a^{-3} -2 z a^{-7} +2 a^{-2} +4 a^{-4} +2 a^{-6} +1 }[/math] |
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