K12a874
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-5 q^2+13 q-24+35 q^{-1} -42 q^{-2} +46 q^{-3} -42 q^{-4} +34 q^{-5} -23 q^{-6} +12 q^{-7} -5 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+12 t^3-33 t^2+59 t-71+59 t^{-1} -33 t^{-2} +12 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-4 z^6-z^4+3 z^2+1 }[/math] |
| Determinant | 283 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8-a^2 z^8+a^6 z^6-3 a^4 z^6-3 a^2 z^6+z^6+2 a^6 z^4-2 a^4 z^4-3 a^2 z^4+2 z^4+3 a^4 z^2-a^2 z^2+z^2-2 a^6+3 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a^5 z^{11}+5 a^3 z^{11}+13 a^6 z^{10}+27 a^4 z^{10}+14 a^2 z^{10}+15 a^7 z^9+20 a^5 z^9+22 a^3 z^9+17 a z^9+11 a^8 z^8-13 a^6 z^8-51 a^4 z^8-15 a^2 z^8+12 z^8+5 a^9 z^7-24 a^7 z^7-58 a^5 z^7-65 a^3 z^7-31 a z^7+5 z^7 a^{-1} +a^{10} z^6-19 a^8 z^6-7 a^6 z^6+29 a^4 z^6-6 a^2 z^6+z^6 a^{-2} -21 z^6-8 a^9 z^5+7 a^7 z^5+41 a^5 z^5+51 a^3 z^5+18 a z^5-7 z^5 a^{-1} -a^{10} z^4+9 a^8 z^4+11 a^6 z^4-3 a^4 z^4+8 a^2 z^4-z^4 a^{-2} +11 z^4+3 a^9 z^3+6 a^7 z^3-2 a^5 z^3-12 a^3 z^3-5 a z^3+2 z^3 a^{-1} -a^8 z^2-5 a^6 z^2-4 a^4 z^2-2 a^2 z^2-2 z^2-4 a^7 z-5 a^5 z-a^3 z+2 a^6+3 a^4 }[/math] |
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