Go for a Wien bridge oscillator, which only requires a gain of 3.
https://en.wikipedia.org/wiki/Wien_bridge_oscillator?useskin=vectorI tried building it one a breadboard, but used the TL072. It did oscillate, but I consider it to be a failure because the frequency was well-out, at 220kHz. I chose lo resistor values, to reduce the effect of the parasitic capacitance of the breadboard. I tried increasing the supply voltage from 5V to 12V, but it made no difference. The TL071 obviously isn't fast enough.
I used the standard Wien bridge circuit, with the classic lightbulb gain control. The only difference was I designed it for a single supply.
f = 1/(2πRC)
R1 and R2, form a potential divider with an output impedance equivalent to their values in parallel, to the non-inverting input, so a resistance of 820/2 = 410R.
R3 = 390R.
For simplicity, consider R to be 400R, which should be near enough.
C = 1nF.
f = 1/(2π*400*10
-9) = 400kHz.
Note: the C1 and C3 are connected to +V, to avoid the risk of the TL071 going into phase inversion (when the functions of the +- inputs exchange, due to the common mode range limits being exceeded). If you're using a different op-amp say one which works with its inputs down to the negative supply, you'll be better off connecting them to 0V. It makes no difference, once the circuit is running, as both rails can be considered to be ground, at AC, since the power supply should have a low impedance C4 AC couples them together, for good measure.
It's also a little distorted, which is evident from the fact that the peaks are asymmetrical, even though the oscilloscope is set to AC coupled.
It might be better if built on a PCB, with a decent layout, but I think a faster op-amp is required.