Elliptic curve isogeny class with Cremona label 53391c (LMFDB label 53391.a)

• Label: 53391c
• Number of curves: $4$
• Conductor: $53391$
• CM: no
• Rank: $1$

Elliptic curves in class 53391c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53391.a4	53391c1	\([1, 1, 1, 656, -13504]\)	\(12167/39\)	\(-100063329951\)	\([2]\)	\(51840\)	\(0.79395\)	\(\Gamma_0(N)\)-optimal
53391.a3	53391c2	\([1, 1, 1, -6189, -164094]\)	\(10218313/1521\)	\(3902469868089\)	\([2, 2]\)	\(103680\)	\(1.1405\)
53391.a2	53391c3	\([1, 1, 1, -26724, 1511562]\)	\(822656953/85683\)	\(219839135902347\)	\([2]\)	\(207360\)	\(1.4871\)
53391.a1	53391c4	\([1, 1, 1, -95174, -11340610]\)	\(37159393753/1053\)	\(2701709908677\)	\([2]\)	\(207360\)	\(1.4871\)

Rank

The elliptic curves in class 53391c have rank \(1\).

Complex multiplication

The elliptic curves in class 53391c do not have complex multiplication.

Modular form 53391.2.a.c

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.