Elliptic curve isogeny class with Cremona label 5929e (LMFDB label 5929.c)

• Label: 5929e
• Number of curves: $4$
• Conductor: $5929$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $1$

Elliptic curves in class 5929e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
5929.c4	5929e1	\([1, -1, 1, -265, 2104]\)	\(-3375\)	\(-607645423\)	\([2]\)	\(1280\)	\(0.39981\)	\(\Gamma_0(N)\)-optimal	\(-7\)
5929.c3	5929e2	\([1, -1, 1, -4500, 117296]\)	\(16581375\)	\(607645423\)	\([2]\)	\(2560\)	\(0.74638\)		\(-28\)
5929.c2	5929e3	\([1, -1, 1, -12970, -695824]\)	\(-3375\)	\(-71488876370527\)	\([2]\)	\(8960\)	\(1.3728\)		\(-7\)
5929.c1	5929e4	\([1, -1, 1, -220485, -39791650]\)	\(16581375\)	\(71488876370527\)	\([2]\)	\(17920\)	\(1.7193\)		\(-28\)

Rank

The elliptic curves in class 5929e have rank \(1\).

Complex multiplication

Each elliptic curve in class 5929e has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 5929.2.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 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.