Elliptic curve isogeny class with LMFDB label 32.a (Cremona label 32a)

• Label: 32.a
• Number of curves: $4$
• Conductor: $32$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Elliptic curves in class 32.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
32.a1	32a3	\([0, 0, 0, -11, -14]\)	\(287496\)	\(512\)	\([2]\)	\(4\)	\(-0.61739\)		\(-16\)
32.a2	32a4	\([0, 0, 0, -11, 14]\)	\(287496\)	\(512\)	\([4]\)	\(4\)	\(-0.61739\)		\(-16\)
32.a3	32a2	\([0, 0, 0, -1, 0]\)	\(1728\)	\(64\)	\([2, 2]\)	\(2\)	\(-0.96396\)		\(-4\)
32.a4	32a1	\([0, 0, 0, 4, 0]\)	\(1728\)	\(-4096\)	\([4]\)	\(1\)	\(-0.61739\)	\(\Gamma_0(N)\)-optimal	\(-4\)

Rank

The elliptic curves in class 32.a have rank \(0\).

Complex multiplication

Each elliptic curve in class 32.a has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 32.2.a.a

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.