Elliptic curve isogeny class with Cremona label 89232u (LMFDB label 89232.bo)

• Label: 89232u
• Number of curves: $4$
• Conductor: $89232$
• CM: no
• Rank: $1$

Elliptic curves in class 89232u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
89232.bo3	89232u1	\([0, 1, 0, -2084, 34620]\)	\(810448/33\)	\(40776882432\)	\([2]\)	\(73728\)	\(0.80174\)	\(\Gamma_0(N)\)-optimal
89232.bo2	89232u2	\([0, 1, 0, -5464, -110044]\)	\(3650692/1089\)	\(5382548481024\)	\([2, 2]\)	\(147456\)	\(1.1483\)
89232.bo4	89232u3	\([0, 1, 0, 14816, -718444]\)	\(36382894/43923\)	\(-434192244135936\)	\([2]\)	\(294912\)	\(1.4949\)
89232.bo1	89232u4	\([0, 1, 0, -79824, -8706060]\)	\(5690357426/891\)	\(8807806605312\)	\([2]\)	\(294912\)	\(1.4949\)

Rank

The elliptic curves in class 89232u have rank \(1\).

Complex multiplication

The elliptic curves in class 89232u do not have complex multiplication.

Modular form 89232.2.a.u

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.