K12a459
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-12+22 q^{-1} -30 q^{-2} +37 q^{-3} -39 q^{-4} +35 q^{-5} -28 q^{-6} +19 q^{-7} -10 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-21 t^2+58 t-79+58 t^{-1} -21 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-3 z^4+z^2+1 }[/math] |
| Determinant | 243 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+4 z^2 a^8+3 a^8-5 z^4 a^6-7 z^2 a^6-3 a^6+2 z^6 a^4+3 z^4 a^4+3 z^2 a^4+z^6 a^2+z^2 a^2+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}-12 z^6 a^{10}+12 z^4 a^{10}-5 z^2 a^{10}+a^{10}+7 z^9 a^9-17 z^7 a^9+10 z^5 a^9-z^3 a^9+7 z^{10} a^8-8 z^8 a^8-17 z^6 a^8+29 z^4 a^8-17 z^2 a^8+3 a^8+3 z^{11} a^7+15 z^9 a^7-58 z^7 a^7+58 z^5 a^7-24 z^3 a^7+4 z a^7+19 z^{10} a^6-33 z^8 a^6-7 z^6 a^6+37 z^4 a^6-21 z^2 a^6+3 a^6+3 z^{11} a^5+28 z^9 a^5-85 z^7 a^5+78 z^5 a^5-28 z^3 a^5+5 z a^5+12 z^{10} a^4-2 z^8 a^4-35 z^6 a^4+35 z^4 a^4-9 z^2 a^4+20 z^9 a^3-33 z^7 a^3+20 z^5 a^3-7 z^3 a^3+2 z a^3+19 z^8 a^2-28 z^6 a^2+12 z^4 a^2-2 a^2+12 z^7 a-12 z^5 a+z^3 a+5 z^6-3 z^4+z^5 a^{-1} }[/math] |
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