Elliptic curve isogeny class with LMFDB label 13475.c (Cremona label 13475e)

• Label: 13475.c
• Number of curves: $4$
• Conductor: $13475$
• CM: no
• Rank: $0$

Elliptic curves in class 13475.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13475.c1	13475e3	\([1, -1, 1, -72505, -7494378]\)	\(22930509321/6875\)	\(12638076171875\)	\([2]\)	\(36864\)	\(1.4920\)
13475.c2	13475e4	\([1, -1, 1, -35755, 2550622]\)	\(2749884201/73205\)	\(134570235078125\)	\([2]\)	\(36864\)	\(1.4920\)
13475.c3	13475e2	\([1, -1, 1, -5130, -83128]\)	\(8120601/3025\)	\(5560753515625\)	\([2, 2]\)	\(18432\)	\(1.1454\)
13475.c4	13475e1	\([1, -1, 1, 995, -9628]\)	\(59319/55\)	\(-101104609375\)	\([2]\)	\(9216\)	\(0.79886\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 13475.c have rank \(0\).

Complex multiplication

The elliptic curves in class 13475.c do not have complex multiplication.

Modular form 13475.2.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 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.