Elliptic curve isogeny class with Cremona label 25921a (LMFDB label 25921.b)

• Label: 25921a
• Number of curves: $4$
• Conductor: $25921$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $1$

Elliptic curves in class 25921a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
25921.b4	25921a1	\([1, -1, 0, -1157, 18920]\)	\(-3375\)	\(-50776309927\)	\([2]\)	\(11264\)	\(0.76861\)	\(\Gamma_0(N)\)-optimal	\(-7\)
25921.b3	25921a2	\([1, -1, 0, -19672, 1066869]\)	\(16581375\)	\(50776309927\)	\([2]\)	\(22528\)	\(1.1152\)		\(-28\)
25921.b2	25921a3	\([1, -1, 0, -56702, -6376161]\)	\(-3375\)	\(-5973782086601623\)	\([2]\)	\(78848\)	\(1.7416\)		\(-7\)
25921.b1	25921a4	\([1, -1, 0, -963937, -364008198]\)	\(16581375\)	\(5973782086601623\)	\([2]\)	\(157696\)	\(2.0881\)		\(-28\)

Rank

The elliptic curves in class 25921a have rank \(1\).

Complex multiplication

Each elliptic curve in class 25921a has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 25921.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.