Properties

Label 89232u
Number of curves 4
Conductor 89232
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("89232.bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 89232u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
89232.bo3 89232u1 [0, 1, 0, -2084, 34620] [2] 73728 \(\Gamma_0(N)\)-optimal
89232.bo2 89232u2 [0, 1, 0, -5464, -110044] [2, 2] 147456  
89232.bo4 89232u3 [0, 1, 0, 14816, -718444] [2] 294912  
89232.bo1 89232u4 [0, 1, 0, -79824, -8706060] [2] 294912  

Rank

sage: E.rank()
 

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

Modular form 89232.2.a.bo

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} + q^{9} + q^{11} - 2q^{15} + 6q^{17} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().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

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.