Elliptic curve isogeny class with Cremona label 74529x (LMFDB label 74529.bj)

• Label: 74529x
• Number of curves: $4$
• Conductor: $74529$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $1$

Elliptic curves in class 74529x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
74529.bj4	74529x1	\([1, -1, 0, -3327, 91664]\)	\(-3375\)	\(-1206929110023\)	\([2]\)	\(75264\)	\(1.0326\)	\(\Gamma_0(N)\)-optimal	\(-7\)
74529.bj3	74529x2	\([1, -1, 0, -56562, 5191577]\)	\(16581375\)	\(1206929110023\)	\([2]\)	\(150528\)	\(1.3792\)		\(-28\)
74529.bj2	74529x3	\([1, -1, 0, -163032, -31114693]\)	\(-3375\)	\(-141994002865095927\)	\([2]\)	\(526848\)	\(2.0056\)		\(-7\)
74529.bj1	74529x4	\([1, -1, 0, -2771547, -1775167822]\)	\(16581375\)	\(141994002865095927\)	\([2]\)	\(1053696\)	\(2.3522\)		\(-28\)

Rank

The elliptic curves in class 74529x have rank \(1\).

Complex multiplication

Each elliptic curve in class 74529x has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 74529.2.a.x

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.