K12n53
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-5 q^5+8 q^4-9 q^3+9 q^2-9 q+7-4 q^{-1} +2 q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^2-14 t+23-14 t^{-1} +3 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^4-2 z^2+1 }[/math] |
| Determinant | 57 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^4 a^{-2} +z^4 a^{-4} +3 z^2 a^{-2} -z^2 a^{-6} -4 z^2+2 a^2+2 a^{-2} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +2 z^9 a^{-1} +5 z^9 a^{-3} +3 z^9 a^{-5} +2 z^8 a^{-4} +3 z^8 a^{-6} +z^8-7 z^7 a^{-1} -19 z^7 a^{-3} -11 z^7 a^{-5} +z^7 a^{-7} -8 z^6 a^{-2} -19 z^6 a^{-4} -13 z^6 a^{-6} -2 z^6+a z^5+10 z^5 a^{-1} +23 z^5 a^{-3} +10 z^5 a^{-5} -4 z^5 a^{-7} +8 z^4 a^{-2} +23 z^4 a^{-4} +16 z^4 a^{-6} +z^4+a z^3-7 z^3 a^{-1} -17 z^3 a^{-3} -5 z^3 a^{-5} +4 z^3 a^{-7} +2 a^2 z^2-10 z^2 a^{-4} -6 z^2 a^{-6} +6 z^2+4 z a^{-1} +6 z a^{-3} +2 z a^{-5} -2 a^2-2 a^{-2} -3 }[/math] |
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