K12a412
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-12+20 q^{-1} -27 q^{-2} +33 q^{-3} -33 q^{-4} +30 q^{-5} -23 q^{-6} +15 q^{-7} -8 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-20 t^2+49 t-65+49 t^{-1} -20 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+4 z^4+5 z^2+1 }[/math] |
| Determinant | 211 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-2 a^8+z^6 a^6+2 z^4 a^6+4 z^2 a^6+2 a^6+2 z^6 a^4+4 z^4 a^4+4 z^2 a^4+a^4+z^6 a^2-z^2 a^2-z^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-10 z^6 a^{10}+10 z^4 a^{10}-3 z^2 a^{10}+5 z^9 a^9-14 z^7 a^9+12 z^5 a^9-5 z^3 a^9+2 z a^9+5 z^{10} a^8-9 z^8 a^8+2 z^6 a^8-z^4 a^8+4 z^2 a^8-2 a^8+2 z^{11} a^7+10 z^9 a^7-38 z^7 a^7+43 z^5 a^7-24 z^3 a^7+6 z a^7+13 z^{10} a^6-23 z^8 a^6+8 z^6 a^6-z^4 a^6+4 z^2 a^6-2 a^6+2 z^{11} a^5+20 z^9 a^5-52 z^7 a^5+42 z^5 a^5-16 z^3 a^5+3 z a^5+8 z^{10} a^4+6 z^8 a^4-34 z^6 a^4+24 z^4 a^4-5 z^2 a^4+a^4+15 z^9 a^3-17 z^7 a^3+z^3 a^3+z a^3+17 z^8 a^2-25 z^6 a^2+11 z^4 a^2-2 z^2 a^2+12 z^7 a-14 z^5 a+3 z^3 a+5 z^6-3 z^4+z^5 a^{-1} }[/math] |
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