Elliptic curve isogeny class with LMFDB label 47089.c (Cremona label 47089a)

• Label: 47089.c
• Number of curves: $4$
• Conductor: $47089$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $1$

Elliptic curves in class 47089.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
47089.c1	47089a4	\([1, -1, 0, -1751122, -891429351]\)	\(16581375\)	\(35813974754127367\)	\([2]\)	\(430080\)	\(2.2374\)		\(-28\)
47089.c2	47089a3	\([1, -1, 0, -103007, -15621040]\)	\(-3375\)	\(-35813974754127367\)	\([2]\)	\(215040\)	\(1.8908\)		\(-7\)
47089.c3	47089a2	\([1, -1, 0, -35737, 2609130]\)	\(16581375\)	\(304413762583\)	\([2]\)	\(61440\)	\(1.2644\)		\(-28\)
47089.c4	47089a1	\([1, -1, 0, -2102, 46143]\)	\(-3375\)	\(-304413762583\)	\([2]\)	\(30720\)	\(0.91786\)	\(\Gamma_0(N)\)-optimal	\(-7\)

Rank

The elliptic curves in class 47089.c have rank \(1\).

Complex multiplication

Each elliptic curve in class 47089.c has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 47089.2.a.c

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.