K12a59
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-20 q^6+30 q^5-38 q^4+42 q^3-39 q^2+33 q-23+13 q^{-1} -5 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-28 t^2+57 t-71+57 t^{-1} -28 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^2+1 }[/math] |
| Determinant | 259 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +3 z^6 a^{-4} +z^6-8 z^4 a^{-2} +9 z^4 a^{-4} -3 z^4 a^{-6} +2 z^4-7 z^2 a^{-2} +11 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} +2 z^2-2 a^{-2} +5 a^{-4} -4 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +9 z^{10} a^{-2} +16 z^{10} a^{-4} +7 z^{10} a^{-6} +15 z^9 a^{-1} +32 z^9 a^{-3} +27 z^9 a^{-5} +10 z^9 a^{-7} +11 z^8 a^{-2} +z^8 a^{-4} +10 z^8 a^{-6} +8 z^8 a^{-8} +12 z^8+5 a z^7-23 z^7 a^{-1} -72 z^7 a^{-3} -59 z^7 a^{-5} -11 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-56 z^6 a^{-2} -63 z^6 a^{-4} -45 z^6 a^{-6} -14 z^6 a^{-8} +z^6 a^{-10} -22 z^6-7 a z^5+8 z^5 a^{-1} +46 z^5 a^{-3} +36 z^5 a^{-5} -3 z^5 a^{-7} -8 z^5 a^{-9} -a^2 z^4+49 z^4 a^{-2} +68 z^4 a^{-4} +47 z^4 a^{-6} +10 z^4 a^{-8} -2 z^4 a^{-10} +15 z^4+3 a z^3-2 z^3 a^{-1} -13 z^3 a^{-3} -3 z^3 a^{-5} +11 z^3 a^{-7} +6 z^3 a^{-9} -18 z^2 a^{-2} -28 z^2 a^{-4} -20 z^2 a^{-6} -4 z^2 a^{-8} +z^2 a^{-10} -5 z^2+z a^{-1} +2 z a^{-3} -2 z a^{-5} -5 z a^{-7} -2 z a^{-9} +2 a^{-2} +5 a^{-4} +4 a^{-6} + a^{-8} +1 }[/math] |
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