Elliptic curve isogeny class with LMFDB label 9747.f (Cremona label 9747a)

• Label: 9747.f
• Number of curves: $4$
• Conductor: $9747$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 9747.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
9747.f1	9747a4	\([0, 0, 1, -97470, 11713457]\)	\(-12288000\)	\(-8334036681507\)	\([]\)	\(18954\)	\(1.5244\)		\(-27\)
9747.f2	9747a2	\([0, 0, 1, -10830, -433832]\)	\(-12288000\)	\(-11432149083\)	\([]\)	\(6318\)	\(0.97506\)		\(-27\)
9747.f3	9747a1	\([0, 0, 1, 0, -1715]\)	\(0\)	\(-1270238787\)	\([]\)	\(2106\)	\(0.42576\)	\(\Gamma_0(N)\)-optimal	\(-3\)
9747.f4	9747a3	\([0, 0, 1, 0, 46298]\)	\(0\)	\(-926004075723\)	\([]\)	\(6318\)	\(0.97506\)		\(-3\)

Rank

The elliptic curves in class 9747.f have rank \(0\).

Complex multiplication

Each elliptic curve in class 9747.f has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 9747.2.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.

\(\left(\begin{array}{rrrr} 1 & 27 & 9 & 3 \\ 27 & 1 & 3 & 9 \\ 9 & 3 & 1 & 3 \\ 3 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.