Elliptic curve isogeny class with Cremona label 5776g (LMFDB label 5776.i)

• Label: 5776g
• Number of curves: $2$
• Conductor: $5776$
• CM: \(\Q(\sqrt{-19}) \)
• Rank: $0$

Elliptic curves in class 5776g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
5776.i2	5776g1	\([0, 0, 0, -608, -5776]\)	\(-884736\)	\(-28094464\)	\([]\)	\(1440\)	\(0.34300\)	\(\Gamma_0(N)\)-optimal	\(-19\)
5776.i1	5776g2	\([0, 0, 0, -219488, 39617584]\)	\(-884736\)	\(-1321728810102784\)	\([]\)	\(27360\)	\(1.8152\)		\(-19\)

Rank

The elliptic curves in class 5776g have rank \(0\).

Complex multiplication

Each elliptic curve in class 5776g has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-19}) \).

Modular form 5776.2.a.g

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.