Elliptic curve isogeny class with LMFDB label 5408.g (Cremona label 5408a)

• Label: 5408.g
• Number of curves: $4$
• Conductor: $5408$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 5408.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
5408.g1	5408a2	\([0, 0, 0, -1859, -30758]\)	\(287496\)	\(2471326208\)	\([2]\)	\(1920\)	\(0.66509\)		\(-16\)
5408.g2	5408a3	\([0, 0, 0, -1859, 30758]\)	\(287496\)	\(2471326208\)	\([2]\)	\(1920\)	\(0.66509\)		\(-16\)
5408.g3	5408a1	\([0, 0, 0, -169, 0]\)	\(1728\)	\(308915776\)	\([2, 2]\)	\(960\)	\(0.31852\)	\(\Gamma_0(N)\)-optimal	\(-4\)
5408.g4	5408a4	\([0, 0, 0, 676, 0]\)	\(1728\)	\(-19770609664\)	\([2]\)	\(1920\)	\(0.66509\)		\(-4\)

Rank

The elliptic curves in class 5408.g have rank \(1\).

Complex multiplication

Each elliptic curve in class 5408.g has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 5408.2.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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.