This curve is due to Noam Elkies and is listed in his 2011 Oberwolfach report Moduli of Marked Elliptic Curves. Elkies gives the rank-4 curve with rational 2-torsion as \((N;a_2,a_4)=(4405696;106,-184)\), corresponding to \(y^2=x^3+106x^2-184x\). Its global minimal model has ainvs \([0,1,0,-3929,93415]\), rank 4, torsion \(\mathbf Z/2\mathbf Z\), and conductor \(4405696\).
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