60558 Echeclus (2000 EC98) also known as 174P/Echeclus is a centaur that occasionally shows a cometary activity.
Outbursts happened in 2005, 2011 and in the first days of December 2017 (see MPML message from Brian Skiff) and confirmation from Richard Miles and JeanFrançois Soulier.
The 2017 outburst is the strongest ever witnessed.
I
simulated 100 clones of this centaur in the past 10^8 days trying to
confirm its possible cometary origin: note that I am not taking into account the non gravitational forces associated to its outburst, not clear to me if they have a considerable effect.
The
first step was to generate clones having orbital parameters distributed
around the nominal ones with 1sigma uncertainty as follows:
JPL SmallBody Database Browser
60558 Echeclus (2000 EC98)
[ show orbit diagram ]
Simulation approach

Algorithm: BulirschStoer (conservative systems)
Integration start epoch: 2458000.5000000 days
Integration stop epoch: 100000000.0000000
Output interval: 100.000
Output precision: medium
Initial timestep: 0.050 days
Accuracy parameter: 1.0000E12
Central mass: 1.0000E+00 solar masses
J_2: 0.0000E+00
J_4: 0.0000E+00
J_6: 0.0000E+00
Ejection distance: 1.0000E+02 AU
Radius of central body: 5.0000E03 AU
Simulation Results
The time (Year) when they entered the solar system was distributed as follows:
Min. 1st Qu. Median Mean 3rd Qu. Max.
263932 124236 73420 91748 41428 5315
In a graphical form:
A look at the nominal asteroid
The nominal asteroid itself has a cometary origin.
60558 Echeclus (2000 EC98)
Classification: Centaur SPKID: 2060558 
[ Ephemeris  Orbit Diagram  Orbital Elements  Physical Parameters  Discovery Circumstances  CloseApproach Data ] 
[ show orbit diagram ]
Orbital Elements at Epoch 2458000.5 (2017Sep04.0) TDB Reference: JPL 85 (heliocentric ecliptic J2000)
 Orbit Determination Parameters
Additional Information

Simulation approach
reference:
J.E.Chambers (1999)
A
Hybrid Symplectic Integrator that Permits Close Encounters between
Massive Bodies''. Monthly Notices of the Royal Astronomical Society, vol
304, pp793799.
Integration parameters
Algorithm: BulirschStoer (conservative systems)
Integration start epoch: 2458000.5000000 days
Integration stop epoch: 100000000.0000000
Output interval: 100.000
Output precision: medium
Initial timestep: 0.050 days
Accuracy parameter: 1.0000E12
Central mass: 1.0000E+00 solar masses
J_2: 0.0000E+00
J_4: 0.0000E+00
J_6: 0.0000E+00
Ejection distance: 1.0000E+02 AU
Radius of central body: 5.0000E03 AU
Simulation Results
 72 out of 100 clones have a cometary orbit (i.e. they came from a distance greater than 100 AU).
 of which: 5 came on a hyperbolic orbit. The one that had the highest speed had a Vinfinity about 3.7 km/s (Vinfinity = 42.1219*sqrt(0.5/a) > the semimajor axis being about 65.7 AU
The time (Year) when they entered the solar system was distributed as follows:
Min. 1st Qu. Median Mean 3rd Qu. Max.
263932 124236 73420 91748 41428 5315
In a graphical form:
A look at the nominal asteroid
The nominal asteroid itself has a cometary origin.
It entered into the solar system at about year 109000 B.C.
In the plot below, the dashed vertical lines correspond to a close approach with Jupiter. All plots in this page have been done with R package ggplot2.
Note that Jupiter was not immediately important.
In its early history, 174P/Echeclus was much more influenced by Saturn as shown here:
Coming back to plots showing the role of Jupiter, we can see these other ones:
A look at the clones  "footprint" diagrams
This is shown here ( I have used the R function stat_density2d  color scale implemented by viridis library):
At
any given time in the past, a clone had a certain perihelium q and a
certain aphelium Q (I disregard the clones when on an hyperbolic
trajectory because Q would be infinite).
Let's
imagine that we plot all possible qQ points in a diagram: the highest
density area is the one where the clones happened to be for most of the
time.
This is shown here ( I have used the R function stat_density2d  color scale implemented by viridis library):