Elliptic curve isogeny class with LMFDB label 45387.e (Cremona label 45387a)

• Label: 45387.e
• Number of curves: $4$
• Conductor: $45387$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 45387.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
45387.e1	45387a4	\([0, 0, 1, -453870, -117699838]\)	\(-12288000\)	\(-841466715980427\)	\([]\)	\(211680\)	\(1.9089\)		\(-27\)
45387.e2	45387a3	\([0, 0, 1, -50430, 4359253]\)	\(-12288000\)	\(-1154275330563\)	\([]\)	\(70560\)	\(1.3596\)		\(-27\)
45387.e3	45387a2	\([0, 0, 1, 0, -465217]\)	\(0\)	\(-93496301775603\)	\([]\)	\(70560\)	\(1.3596\)		\(-3\)
45387.e4	45387a1	\([0, 0, 1, 0, 17230]\)	\(0\)	\(-128252814507\)	\([]\)	\(23520\)	\(0.81032\)	\(\Gamma_0(N)\)-optimal	\(-3\)

Rank

The elliptic curves in class 45387.e have rank \(1\).

Complex multiplication

Each elliptic curve in class 45387.e has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 45387.2.a.e

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.