Elliptic curve isogeny class with LMFDB label 49.a (Cremona label 49a)

• Label: 49.a
• Number of curves: $4$
• Conductor: $49$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $0$

Elliptic curves in class 49.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
49.a1	49a4	\([1, -1, 0, -1822, 30393]\)	\(16581375\)	\(40353607\)	\([2]\)	\(14\)	\(0.52039\)		\(-28\)
49.a2	49a3	\([1, -1, 0, -107, 552]\)	\(-3375\)	\(-40353607\)	\([2]\)	\(7\)	\(0.17382\)		\(-7\)
49.a3	49a2	\([1, -1, 0, -37, -78]\)	\(16581375\)	\(343\)	\([2]\)	\(2\)	\(-0.45256\)		\(-28\)
49.a4	49a1	\([1, -1, 0, -2, -1]\)	\(-3375\)	\(-343\)	\([2]\)	\(1\)	\(-0.79914\)	\(\Gamma_0(N)\)-optimal	\(-7\)

Rank

The elliptic curves in class 49.a have rank \(0\).

Complex multiplication

Each elliptic curve in class 49.a has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 49.2.a.a

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.