Elliptic curve isogeny class with LMFDB label 74529.t (Cremona label 74529e)

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

Elliptic curves in class 74529.t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
74529.t1	74529e1	\([0, 0, 1, 0, -649763]\)	\(0\)	\(-182386784716227\)	\([]\)	\(123552\)	\(1.4153\)	\(\Gamma_0(N)\)-optimal	\(-3\)
74529.t2	74529e2	\([0, 0, 1, 0, 17543594]\)	\(0\)	\(-132959966058129483\)	\([]\)	\(370656\)	\(1.9646\)		\(-3\)

Rank

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

Complex multiplication

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

Modular form 74529.2.a.t

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.