Properties

Label 151725cj
Number of curves 4
Conductor 151725
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("151725.cx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 151725cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
151725.cx4 151725cj1 [1, 0, 1, 100999, 20787023] [2] 1769472 \(\Gamma_0(N)\)-optimal
151725.cx3 151725cj2 [1, 0, 1, -802126, 226699523] [2, 2] 3538944  
151725.cx1 151725cj3 [1, 0, 1, -12181501, 16362653273] [2] 7077888  
151725.cx2 151725cj4 [1, 0, 1, -3872751, -2727241727] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 151725cj have rank \(1\).

Modular form 151725.2.a.cx

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} + q^{6} + q^{7} - 3q^{8} + q^{9} - q^{12} + 6q^{13} + q^{14} - q^{16} + q^{18} + 4q^{19} + O(q^{20}) \)

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.