Elliptic curve isogeny class with Cremona label 10800cz (LMFDB label 10800.bo)

• Label: 10800cz
• Number of curves: $4$
• Conductor: $10800$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 10800cz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
10800.bo3	10800cz1	\([0, 0, 0, 0, -2000]\)	\(0\)	\(-1728000000\)	\([]\)	\(3456\)	\(0.45140\)	\(\Gamma_0(N)\)-optimal	\(-3\)
10800.bo2	10800cz2	\([0, 0, 0, -12000, -506000]\)	\(-12288000\)	\(-15552000000\)	\([]\)	\(10368\)	\(1.0007\)		\(-27\)
10800.bo4	10800cz3	\([0, 0, 0, 0, 54000]\)	\(0\)	\(-1259712000000\)	\([]\)	\(10368\)	\(1.0007\)		\(-3\)
10800.bo1	10800cz4	\([0, 0, 0, -108000, 13662000]\)	\(-12288000\)	\(-11337408000000\)	\([]\)	\(31104\)	\(1.5500\)		\(-27\)

Rank

The elliptic curves in class 10800cz have rank \(1\).

Complex multiplication

Each elliptic curve in class 10800cz has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 10800.2.a.cz

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.