K12a1258
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-13 q^3+19 q^2-23 q+25-23 q^{-1} +19 q^{-2} -13 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+4 t^4-10 t^3+19 t^2-28 t+33-28 t^{-1} +19 t^{-2} -10 t^{-3} +4 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-6 z^8-13 z^6-11 z^4-3 z^2+1 }[/math] |
| Determinant | 157 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -8 z^8+6 a^2 z^6+6 z^6 a^{-2} -25 z^6+13 a^2 z^4+13 z^4 a^{-2} -37 z^4+11 a^2 z^2+11 z^2 a^{-2} -25 z^2+3 a^2+3 a^{-2} -5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+5 z^{10} a^{-2} +10 z^{10}+6 a^3 z^9+3 a z^9+3 z^9 a^{-1} +6 z^9 a^{-3} +5 a^4 z^8-11 a^2 z^8-12 z^8 a^{-2} +5 z^8 a^{-4} -33 z^8+3 a^5 z^7-14 a^3 z^7-15 a z^7-16 z^7 a^{-1} -15 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-12 a^4 z^6+15 a^2 z^6+21 z^6 a^{-2} -12 z^6 a^{-4} +z^6 a^{-6} +62 z^6-8 a^5 z^5+12 a^3 z^5+24 a z^5+30 z^5 a^{-1} +18 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+8 a^4 z^4-15 a^2 z^4-24 z^4 a^{-2} +8 z^4 a^{-4} -3 z^4 a^{-6} -61 z^4+5 a^5 z^3-5 a^3 z^3-14 a z^3-23 z^3 a^{-1} -14 z^3 a^{-3} +5 z^3 a^{-5} +2 a^6 z^2-3 a^4 z^2+10 a^2 z^2+12 z^2 a^{-2} -2 z^2 a^{-4} +2 z^2 a^{-6} +31 z^2-a^5 z+3 a z+5 z a^{-1} +3 z a^{-3} -3 a^2-3 a^{-2} -5 }[/math] |
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