Elliptic curve isogeny class with LMFDB label 27.a (Cremona label 27a)

• Label: 27.a
• Number of curves: $4$
• Conductor: $27$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 27.a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality	CM discriminant
27.a1	27a2	[0, 0, 1, -270, -1708]	[]	3		-27
27.a2	27a4	[0, 0, 1, -30, 63]	[3]	9		-27
27.a3	27a1	[0, 0, 1, 0, -7]	[3]	1	\(\Gamma_0(N)\)-optimal	-3
27.a4	27a3	[0, 0, 1, 0, 0]	[3]	3		-3

Rank

The elliptic curves in class 27.a have rank \(0\).

Complex multiplication

Each elliptic curve in class 27.a has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 27.2.a.a

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.