Murmurations of elliptic curves over Q ordered by naive height

Each blue/red dot at (p,a_p) records the average of a_p(E) over elliptic curves E/Q of root number w(E)=+1/-1 with naive height max(4|A|³,27|B|²) in a varying dyadic interval.

Each purple dot at (p,a_p) records the average of w(E)a_p(E) over elliptic curves E/Q with naive height max(4|A|³,27|B|²) in a varying dyadic interval.

Each purple dot at (p,a_p) records the average of w(E)a_p(E) over elliptic curves E/Q with naive height max(4|A|³,27|B|²) in a varying dyadic interval. The green line shows the least squares fit using a piecewise polynomial function