Elliptic curve isogeny class with LMFDB label 2275.e (Cremona label 2275c)

• Label: 2275.e
• Number of curves: $4$
• Conductor: $2275$
• CM: no
• Rank: $0$

Elliptic curves in class 2275.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2275.e1	2275c3	\([1, -1, 0, -9917, -359384]\)	\(6903498885921/374712065\)	\(5854876015625\)	\([2]\)	\(3072\)	\(1.2058\)
2275.e2	2275c2	\([1, -1, 0, -1792, 22491]\)	\(40743095121/10144225\)	\(158503515625\)	\([2, 2]\)	\(1536\)	\(0.85927\)
2275.e3	2275c1	\([1, -1, 0, -1667, 26616]\)	\(32798729601/3185\)	\(49765625\)	\([2]\)	\(768\)	\(0.51270\)	\(\Gamma_0(N)\)-optimal
2275.e4	2275c4	\([1, -1, 0, 4333, 138866]\)	\(575722725759/874680625\)	\(-13666884765625\)	\([2]\)	\(3072\)	\(1.2058\)

Rank

The elliptic curves in class 2275.e have rank \(0\).

Complex multiplication

The elliptic curves in class 2275.e do not have complex multiplication.

Modular form 2275.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.