Elliptic curve isogeny class with Cremona label 23232cb (LMFDB label 23232.cl)

• Label: 23232cb
• Number of curves: $4$
• Conductor: $23232$
• CM: no
• Rank: $1$

Elliptic curves in class 23232cb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23232.cl3	23232cb1	\([0, 1, 0, -5969, 169167]\)	\(810448/33\)	\(957833428992\)	\([2]\)	\(30720\)	\(1.0648\)	\(\Gamma_0(N)\)-optimal
23232.cl2	23232cb2	\([0, 1, 0, -15649, -529729]\)	\(3650692/1089\)	\(126434012626944\)	\([2, 2]\)	\(61440\)	\(1.4114\)
23232.cl4	23232cb3	\([0, 1, 0, 42431, -3491809]\)	\(36382894/43923\)	\(-10199010351906816\)	\([2]\)	\(122880\)	\(1.7579\)
23232.cl1	23232cb4	\([0, 1, 0, -228609, -42142113]\)	\(5690357426/891\)	\(206892020662272\)	\([2]\)	\(122880\)	\(1.7579\)

Rank

The elliptic curves in class 23232cb have rank \(1\).

Complex multiplication

The elliptic curves in class 23232cb do not have complex multiplication.

Modular form 23232.2.a.cb

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.