Elliptic curve isogeny class with Cremona label 1425a (LMFDB label 1425.a)

• Label: 1425a
• Number of curves: $4$
• Conductor: $1425$
• CM: no
• Rank: $1$

Elliptic curves in class 1425a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1425.a3	1425a1	\([1, 1, 1, -38, -94]\)	\(389017/57\)	\(890625\)	\([2]\)	\(192\)	\(-0.13344\)	\(\Gamma_0(N)\)-optimal
1425.a2	1425a2	\([1, 1, 1, -163, 656]\)	\(30664297/3249\)	\(50765625\)	\([2, 2]\)	\(384\)	\(0.21314\)
1425.a1	1425a3	\([1, 1, 1, -2538, 48156]\)	\(115714886617/1539\)	\(24046875\)	\([2]\)	\(768\)	\(0.55971\)
1425.a4	1425a4	\([1, 1, 1, 212, 3656]\)	\(67419143/390963\)	\(-6108796875\)	\([2]\)	\(768\)	\(0.55971\)

Rank

The elliptic curves in class 1425a have rank \(1\).

Complex multiplication

The elliptic curves in class 1425a do not have complex multiplication.

Modular form 1425.2.a.a

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.