K12a1212
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-11 q^6+19 q^5-28 q^4+34 q^3-36 q^2+34 q-27+19 q^{-1} -11 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-6 t^4+16 t^3-29 t^2+41 t-45+41 t^{-1} -29 t^{-2} +16 t^{-3} -6 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+4 z^8+3 z^6-3 z^4-2 z^2+1 }[/math] |
| Determinant | 231 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +6 z^8 a^{-2} -z^8 a^{-4} -z^8+11 z^6 a^{-2} -4 z^6 a^{-4} -4 z^6+3 z^4 a^{-2} -3 z^4 a^{-4} -3 z^4-8 z^2 a^{-2} +3 z^2 a^{-4} +3 z^2-4 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-1} +4 z^{11} a^{-3} +21 z^{10} a^{-2} +11 z^{10} a^{-4} +10 z^{10}+10 a z^9+10 z^9 a^{-1} +15 z^9 a^{-3} +15 z^9 a^{-5} +5 a^2 z^8-54 z^8 a^{-2} -9 z^8 a^{-4} +15 z^8 a^{-6} -25 z^8+a^3 z^7-31 a z^7-58 z^7 a^{-1} -54 z^7 a^{-3} -17 z^7 a^{-5} +11 z^7 a^{-7} -14 a^2 z^6+37 z^6 a^{-2} -10 z^6 a^{-4} -18 z^6 a^{-6} +5 z^6 a^{-8} +10 z^6-2 a^3 z^5+26 a z^5+65 z^5 a^{-1} +47 z^5 a^{-3} -4 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +8 a^2 z^4+8 z^4 a^{-2} +11 z^4 a^{-4} +z^4 a^{-6} -4 z^4 a^{-8} +10 z^4-6 a z^3-21 z^3 a^{-1} -9 z^3 a^{-3} +9 z^3 a^{-5} +3 z^3 a^{-7} -17 z^2 a^{-2} -5 z^2 a^{-4} +3 z^2 a^{-6} -9 z^2-2 z a^{-3} -2 z a^{-5} +4 a^{-2} +2 a^{-4} +3 }[/math] |
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