K12a492
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+10 q^4-17 q^3+25 q^2-30 q+31-29 q^{-1} +23 q^{-2} -15 q^{-3} +8 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+15 t^2-47 t+69-47 t^{-1} +15 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+3 z^4-5 z^2+1 }[/math] |
| Determinant | 197 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4-a^4+3 z^4 a^2+z^2 a^2-z^6+z^4+2 z^2+2-z^6 a^{-2} -2 z^4 a^{-2} -6 z^2 a^{-2} -3 a^{-2} +z^4 a^{-4} +z^2 a^{-4} +2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+7 z^{10} a^{-2} +12 z^{10}+6 a^3 z^9+10 a z^9+15 z^9 a^{-1} +11 z^9 a^{-3} +5 a^4 z^8-2 a^2 z^8-4 z^8 a^{-2} +9 z^8 a^{-4} -20 z^8+3 a^5 z^7-7 a^3 z^7-26 a z^7-47 z^7 a^{-1} -27 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-8 a^4 z^6-4 a^2 z^6-21 z^6 a^{-2} -23 z^6 a^{-4} +z^6 a^{-6} +8 z^6-7 a^5 z^5+26 a z^5+52 z^5 a^{-1} +25 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+a^4 z^4+a^2 z^4+34 z^4 a^{-2} +20 z^4 a^{-4} -2 z^4 a^{-6} +9 z^4+5 a^5 z^3-14 a z^3-22 z^3 a^{-1} -11 z^3 a^{-3} +2 z^3 a^{-5} +3 a^6 z^2+3 a^4 z^2-a^2 z^2-17 z^2 a^{-2} -9 z^2 a^{-4} -9 z^2-a^5 z+a^3 z+2 a z+2 z a^{-1} +2 z a^{-3} -a^6-a^4+3 a^{-2} +2 a^{-4} +2 }[/math] |
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