K12a483
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-6 q^2+16 q-28+42 q^{-1} -51 q^{-2} +54 q^{-3} -50 q^{-4} +40 q^{-5} -27 q^{-6} +14 q^{-7} -5 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-35 t^2+75 t-95+75 t^{-1} -35 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6-z^4+1 }[/math] |
| Determinant | 335 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8-3 z^4 a^6-2 z^2 a^6+a^6+3 z^6 a^4+5 z^4 a^4-3 a^4-z^8 a^2-3 z^6 a^2-4 z^4 a^2+z^2 a^2+3 a^2+z^6+z^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a^5 z^{11}+5 a^3 z^{11}+16 a^6 z^{10}+33 a^4 z^{10}+17 a^2 z^{10}+20 a^7 z^9+42 a^5 z^9+45 a^3 z^9+23 a z^9+13 a^8 z^8-5 a^6 z^8-35 a^4 z^8-a^2 z^8+16 z^8+5 a^9 z^7-35 a^7 z^7-112 a^5 z^7-115 a^3 z^7-37 a z^7+6 z^7 a^{-1} +a^{10} z^6-21 a^8 z^6-36 a^6 z^6-37 a^4 z^6-48 a^2 z^6+z^6 a^{-2} -24 z^6-6 a^9 z^5+27 a^7 z^5+89 a^5 z^5+78 a^3 z^5+17 a z^5-5 z^5 a^{-1} -a^{10} z^4+15 a^8 z^4+36 a^6 z^4+43 a^4 z^4+33 a^2 z^4+10 z^4+2 a^9 z^3-12 a^7 z^3-29 a^5 z^3-18 a^3 z^3-3 a z^3-5 a^8 z^2-9 a^6 z^2-4 a^4 z^2+2 a^7 z+4 a^5 z+2 a^3 z-a^6-3 a^4-3 a^2 }[/math] |
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