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

• Label: 74529.x
• Number of curves: $2$
• Conductor: $74529$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 74529.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
74529.x1	74529c2	\([0, 0, 1, 0, -726658]\)	\(0\)	\(-228109601794347\)	\([]\)	\(127008\)	\(1.4340\)		\(-3\)
74529.x2	74529c1	\([0, 0, 1, 0, 26913]\)	\(0\)	\(-312907547043\)	\([]\)	\(42336\)	\(0.88465\)	\(\Gamma_0(N)\)-optimal	\(-3\)

Rank

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

Complex multiplication

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

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.