The waveform is what you can expect when measuring the oscillator output with a regular oscilloscope probe, most likely using a long ground clip cable.
It mainly shows the limitations of your measurement equipment, respectively your way to use it. Simply impossible to get trustworthy rise and fall time measurement this way.
To suggest better ways, we should know about your oscilloscope specification and available probes.
For almost perfect waveforms, I would use a self-made 10:1 resistive probe, small 450 (or 470) ohms series resistor, 50 ohm coaxial cable, 50 ohm terminated oscilloscope input.
Next best, a good passive 10:1 probe with "bayonet" ground tip.