Properties

Label 189525bi
Number of curves 4
Conductor 189525
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("189525.bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189525bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
189525.bo3 189525bi1 [1, 0, 1, -22751, -1253227] [2] 580608 \(\Gamma_0(N)\)-optimal
189525.bo2 189525bi2 [1, 0, 1, -67876, 5244773] [2, 2] 1161216  
189525.bo1 189525bi3 [1, 0, 1, -1015501, 393771023] [2] 2322432  
189525.bo4 189525bi4 [1, 0, 1, 157749, 32771023] [2] 2322432  

Rank

sage: E.rank()
 

The elliptic curves in class 189525bi have rank \(1\).

Modular form 189525.2.a.bo

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} + q^{6} - q^{7} - 3q^{8} + q^{9} - q^{12} - 6q^{13} - q^{14} - q^{16} - 2q^{17} + q^{18} + O(q^{20}) \)

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.