Elliptic curve isogeny class with LMFDB label 22707.c (Cremona label 22707a)

• Label: 22707.c
• Number of curves: $4$
• Conductor: $22707$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 22707.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
22707.c1	22707a4	\([0, 0, 1, -227070, -41650315]\)	\(-12288000\)	\(-105371166845187\)	\([]\)	\(75600\)	\(1.7358\)		\(-27\)
22707.c2	22707a3	\([0, 0, 1, -25230, 1542604]\)	\(-12288000\)	\(-144542067003\)	\([]\)	\(25200\)	\(1.1865\)		\(-27\)
22707.c3	22707a2	\([0, 0, 1, 0, -164626]\)	\(0\)	\(-11707907427243\)	\([]\)	\(25200\)	\(1.1865\)		\(-3\)
22707.c4	22707a1	\([0, 0, 1, 0, 6097]\)	\(0\)	\(-16060229667\)	\([]\)	\(8400\)	\(0.63718\)	\(\Gamma_0(N)\)-optimal	\(-3\)

Rank

The elliptic curves in class 22707.c have rank \(1\).

Complex multiplication

Each elliptic curve in class 22707.c has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 22707.2.a.c

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.