Elliptic curve isogeny class with LMFDB label 9248.f (Cremona label 9248e)

• Label: 9248.f
• Number of curves: $4$
• Conductor: $9248$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Elliptic curves in class 9248.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
9248.f1	9248e2	\([0, 0, 0, -3179, -68782]\)	\(287496\)	\(12358435328\)	\([2]\)	\(5120\)	\(0.79922\)		\(-16\)
9248.f2	9248e3	\([0, 0, 0, -3179, 68782]\)	\(287496\)	\(12358435328\)	\([2]\)	\(5120\)	\(0.79922\)		\(-16\)
9248.f3	9248e1	\([0, 0, 0, -289, 0]\)	\(1728\)	\(1544804416\)	\([2, 2]\)	\(2560\)	\(0.45265\)	\(\Gamma_0(N)\)-optimal	\(-4\)
9248.f4	9248e4	\([0, 0, 0, 1156, 0]\)	\(1728\)	\(-98867482624\)	\([2]\)	\(5120\)	\(0.79922\)		\(-4\)

Rank

The elliptic curves in class 9248.f have rank \(0\).

Complex multiplication

Each elliptic curve in class 9248.f has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 9248.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.