K12a309
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-12 q^5+21 q^4-30 q^3+37 q^2-39 q+36-29 q^{-1} +20 q^{-2} -10 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+21 t^2-58 t+81-58 t^{-1} +21 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+3 z^4-z^2+1 }[/math] |
| Determinant | 245 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6+2 a^2 z^4-4 z^4 a^{-2} +3 z^4 a^{-4} +2 z^4-a^4 z^2-6 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} +4 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +20 z^{10} a^{-2} +9 z^{10} a^{-4} +11 z^{10}+17 a z^9+29 z^9 a^{-1} +22 z^9 a^{-3} +10 z^9 a^{-5} +15 a^2 z^8-31 z^8 a^{-2} -11 z^8 a^{-4} +5 z^8 a^{-6} +9 a^3 z^7-29 a z^7-92 z^7 a^{-1} -82 z^7 a^{-3} -27 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-24 a^2 z^6-23 z^6 a^{-2} -22 z^6 a^{-4} -13 z^6 a^{-6} -42 z^6+a^5 z^5-10 a^3 z^5+24 a z^5+92 z^5 a^{-1} +80 z^5 a^{-3} +21 z^5 a^{-5} -2 z^5 a^{-7} -4 a^4 z^4+20 a^2 z^4+52 z^4 a^{-2} +33 z^4 a^{-4} +10 z^4 a^{-6} +53 z^4-a^5 z^3+4 a^3 z^3-11 a z^3-40 z^3 a^{-1} -31 z^3 a^{-3} -6 z^3 a^{-5} +z^3 a^{-7} +a^4 z^2-7 a^2 z^2-23 z^2 a^{-2} -12 z^2 a^{-4} -3 z^2 a^{-6} -22 z^2+2 a z+6 z a^{-1} +5 z a^{-3} +z a^{-5} +2 a^{-2} + a^{-4} +2 }[/math] |
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