Elliptic curve isogeny class with LMFDB label 1225.c (Cremona label 1225b)

• Label: 1225.c
• Number of curves: $4$
• Conductor: $1225$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $0$

Elliptic curves in class 1225.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
1225.c1	1225b4	\([1, -1, 1, -45555, 3753572]\)	\(16581375\)	\(630525109375\)	\([2]\)	\(2016\)	\(1.3251\)		\(-28\)
1225.c2	1225b3	\([1, -1, 1, -2680, 66322]\)	\(-3375\)	\(-630525109375\)	\([2]\)	\(1008\)	\(0.97854\)		\(-7\)
1225.c3	1225b2	\([1, -1, 1, -930, -10678]\)	\(16581375\)	\(5359375\)	\([2]\)	\(288\)	\(0.35215\)		\(-28\)
1225.c4	1225b1	\([1, -1, 1, -55, -178]\)	\(-3375\)	\(-5359375\)	\([2]\)	\(144\)	\(0.0055806\)	\(\Gamma_0(N)\)-optimal	\(-7\)

Rank

The elliptic curves in class 1225.c have rank \(0\).

Complex multiplication

Each elliptic curve in class 1225.c has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 1225.2.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.