Elliptic curve isogeny class with LMFDB label 28224.dw (Cremona label 28224bn)

• Label: 28224.dw
• Number of curves: $4$
• Conductor: $28224$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $1$

Elliptic curves in class 28224.dw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
28224.dw1	28224bn4	\([0, 0, 0, -1049580, -413855568]\)	\(16581375\)	\(7711694390034432\)	\([2]\)	\(229376\)	\(2.1094\)		\(-28\)
28224.dw2	28224bn3	\([0, 0, 0, -61740, -7260624]\)	\(-3375\)	\(-7711694390034432\)	\([2]\)	\(114688\)	\(1.7628\)		\(-7\)
28224.dw3	28224bn2	\([0, 0, 0, -21420, 1206576]\)	\(16581375\)	\(65548320768\)	\([2]\)	\(32768\)	\(1.1365\)		\(-28\)
28224.dw4	28224bn1	\([0, 0, 0, -1260, 21168]\)	\(-3375\)	\(-65548320768\)	\([2]\)	\(16384\)	\(0.78989\)	\(\Gamma_0(N)\)-optimal	\(-7\)

Rank

The elliptic curves in class 28224.dw have rank \(1\).

Complex multiplication

Each elliptic curve in class 28224.dw has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 28224.2.a.dw

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.