Elliptic curve isogeny class with LMFDB label 49923.g (Cremona label 49923d)

• Label: 49923.g
• Number of curves: $4$
• Conductor: $49923$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 49923.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
49923.g1	49923d4	\([0, 0, 1, -499230, 135778079]\)	\(-12288000\)	\(-1119810500041203\)	\([]\)	\(235872\)	\(1.9327\)		\(-27\)
49923.g2	49923d2	\([0, 0, 1, -55470, -5028818]\)	\(-12288000\)	\(-1536091220907\)	\([]\)	\(78624\)	\(1.3834\)		\(-27\)
49923.g3	49923d1	\([0, 0, 1, 0, -19877]\)	\(0\)	\(-170676802323\)	\([]\)	\(26208\)	\(0.83414\)	\(\Gamma_0(N)\)-optimal	\(-3\)
49923.g4	49923d3	\([0, 0, 1, 0, 536672]\)	\(0\)	\(-124423388893467\)	\([]\)	\(78624\)	\(1.3834\)		\(-3\)

Rank

The elliptic curves in class 49923.g have rank \(0\).

Complex multiplication

Each elliptic curve in class 49923.g has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 49923.2.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.

\(\left(\begin{array}{rrrr} 1 & 27 & 9 & 3 \\ 27 & 1 & 3 & 9 \\ 9 & 3 & 1 & 3 \\ 3 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.