Elliptic curve isogeny class with Cremona label 4563g (LMFDB label 4563.e)

• Label: 4563g
• Number of curves: $4$
• Conductor: $4563$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 4563g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
4563.e4	4563g1	\([0, 0, 1, 0, 549]\)	\(0\)	\(-130323843\)	\([]\)	\(684\)	\(0.23601\)	\(\Gamma_0(N)\)-optimal	\(-3\)
4563.e3	4563g2	\([0, 0, 1, 0, -14830]\)	\(0\)	\(-95006081547\)	\([]\)	\(2052\)	\(0.78532\)		\(-3\)
4563.e2	4563g3	\([0, 0, 1, -5070, 138960]\)	\(-12288000\)	\(-1172914587\)	\([]\)	\(2052\)	\(0.78532\)		\(-27\)
4563.e1	4563g4	\([0, 0, 1, -45630, -3751927]\)	\(-12288000\)	\(-855054733923\)	\([]\)	\(6156\)	\(1.3346\)		\(-27\)

Rank

The elliptic curves in class 4563g have rank \(0\).

Complex multiplication

Each elliptic curve in class 4563g has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 4563.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.