Elliptic curve isogeny class with LMFDB label 74529.r (Cremona label 74529h)

• Label: 74529.r
• Number of curves: $2$
• Conductor: $74529$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 74529.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
74529.r1	74529h1	\([0, 0, 1, 0, -2449106]\)	\(0\)	\(-2591187397063083\)	\([]\)	\(235872\)	\(1.6365\)	\(\Gamma_0(N)\)-optimal	\(-3\)
74529.r2	74529h2	\([0, 0, 1, 0, 66125855]\)	\(0\)	\(-1888975612458987507\)	\([]\)	\(707616\)	\(2.1858\)		\(-3\)

Rank

The elliptic curves in class 74529.r have rank \(0\).

Complex multiplication

Each elliptic curve in class 74529.r has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 74529.2.a.r

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.