Elliptic curve isogeny class with LMFDB label 52855.e (Cremona label 52855j)

• Label: 52855.e
• Number of curves: $4$
• Conductor: $52855$
• CM: no
• Rank: $2$

Elliptic curves in class 52855.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
52855.e1	52855j4	\([1, -1, 0, -56879, -5205722]\)	\(22930509321/6875\)	\(6101587806875\)	\([2]\)	\(115200\)	\(1.4313\)
52855.e2	52855j3	\([1, -1, 0, -28049, 1773060]\)	\(2749884201/73205\)	\(64969706967605\)	\([2]\)	\(115200\)	\(1.4313\)
52855.e3	52855j2	\([1, -1, 0, -4024, -57645]\)	\(8120601/3025\)	\(2684698635025\)	\([2, 2]\)	\(57600\)	\(1.0848\)
52855.e4	52855j1	\([1, -1, 0, 781, -6712]\)	\(59319/55\)	\(-48812702455\)	\([2]\)	\(28800\)	\(0.73818\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 52855.e have rank \(2\).

Complex multiplication

The elliptic curves in class 52855.e do not have complex multiplication.

Modular form 52855.2.a.e

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.