K12a407
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-12+22 q^{-1} -31 q^{-2} +38 q^{-3} -40 q^{-4} +37 q^{-5} -29 q^{-6} +20 q^{-7} -11 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-21 t^2+60 t-83+60 t^{-1} -21 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-3 z^4+3 z^2+1 }[/math] |
| Determinant | 251 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+4 z^2 a^8+2 a^8-5 z^4 a^6-6 z^2 a^6-2 a^6+2 z^6 a^4+3 z^4 a^4+4 z^2 a^4+a^4+z^6 a^2+z^2 a^2+a^2-z^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-3 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+4 z^8 a^{10}-11 z^6 a^{10}+10 z^4 a^{10}-4 z^2 a^{10}+a^{10}+8 z^9 a^9-21 z^7 a^9+18 z^5 a^9-9 z^3 a^9+3 z a^9+8 z^{10} a^8-11 z^8 a^8-12 z^6 a^8+22 z^4 a^8-11 z^2 a^8+2 a^8+3 z^{11} a^7+19 z^9 a^7-72 z^7 a^7+77 z^5 a^7-37 z^3 a^7+7 z a^7+20 z^{10} a^6-32 z^8 a^6-14 z^6 a^6+40 z^4 a^6-18 z^2 a^6+2 a^6+3 z^{11} a^5+31 z^9 a^5-92 z^7 a^5+83 z^5 a^5-30 z^3 a^5+4 z a^5+12 z^{10} a^4+2 z^8 a^4-45 z^6 a^4+43 z^4 a^4-12 z^2 a^4+a^4+20 z^9 a^3-30 z^7 a^3+14 z^5 a^3-3 z^3 a^3+z a^3+19 z^8 a^2-27 z^6 a^2+12 z^4 a^2-z^2 a^2-a^2+12 z^7 a-12 z^5 a+2 z^3 a+5 z^6-3 z^4+z^5 a^{-1} }[/math] |
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