Elliptic curve isogeny class with LMFDB label 112896.d (Cremona label 112896cc)

• Label: 112896.d
• Number of curves: $2$
• Conductor: $112896$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 112896.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
112896.d1	112896cc1	\([0, 0, 0, -882, 0]\)	\(1728\)	\(43912253952\)	\([2]\)	\(98304\)	\(0.73159\)	\(\Gamma_0(N)\)-optimal	\(-4\)
112896.d2	112896cc2	\([0, 0, 0, 3528, 0]\)	\(1728\)	\(-2810384252928\)	\([2]\)	\(196608\)	\(1.0782\)		\(-4\)

Rank

The elliptic curves in class 112896.d have rank \(1\).

Complex multiplication

Each elliptic curve in class 112896.d has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 112896.2.a.d

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.