Elliptic curve isogeny class with LMFDB label 112896.f (Cremona label 112896u)

• Label: 112896.f
• Number of curves: $2$
• Conductor: $112896$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Elliptic curves in class 112896.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
112896.f1	112896u2	\([0, 0, 0, -8232, 0]\)	\(1728\)	\(35702288842752\)	\([2]\)	\(401408\)	\(1.2900\)		\(-4\)
112896.f2	112896u1	\([0, 0, 0, 2058, 0]\)	\(1728\)	\(-557848263168\)	\([2]\)	\(200704\)	\(0.94341\)	\(\Gamma_0(N)\)-optimal	\(-4\)

Rank

The elliptic curves in class 112896.f have rank \(0\).

Complex multiplication

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

Modular form 112896.2.a.f

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.