Elliptic curve isogeny class with Cremona label 13650cm (LMFDB label 13650.cn)

• Label: 13650cm
• Number of curves: $4$
• Conductor: $13650$
• CM: no
• Rank: $1$

Elliptic curves in class 13650cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13650.cn4	13650cm1	\([1, 0, 0, 162, 26292]\)	\(30080231/19110000\)	\(-298593750000\)	\([2]\)	\(18432\)	\(0.88091\)	\(\Gamma_0(N)\)-optimal
13650.cn3	13650cm2	\([1, 0, 0, -12338, 513792]\)	\(13293525831769/365192100\)	\(5706126562500\)	\([2, 2]\)	\(36864\)	\(1.2275\)
13650.cn2	13650cm3	\([1, 0, 0, -28588, -1127458]\)	\(165369706597369/60703354530\)	\(948489914531250\)	\([2]\)	\(73728\)	\(1.5741\)
13650.cn1	13650cm4	\([1, 0, 0, -196088, 33405042]\)	\(53365044437418169/41984670\)	\(656010468750\)	\([2]\)	\(73728\)	\(1.5741\)

Rank

The elliptic curves in class 13650cm have rank \(1\).

Complex multiplication

The elliptic curves in class 13650cm do not have complex multiplication.

Modular form 13650.2.a.cm

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.