Properties

Label 63525q
Number of curves 4
Conductor 63525
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("63525.bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 63525q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63525.bw3 63525q1 [1, 1, 0, -7625, -246000] [2] 138240 \(\Gamma_0(N)\)-optimal
63525.bw2 63525q2 [1, 1, 0, -22750, 1009375] [2, 2] 276480  
63525.bw4 63525q3 [1, 1, 0, 52875, 6378750] [2] 552960  
63525.bw1 63525q4 [1, 1, 0, -340375, 76286500] [2] 552960  

Rank

sage: E.rank()
 

The elliptic curves in class 63525q have rank \(1\).

Modular form 63525.2.a.bw

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} - q^{6} + q^{7} - 3q^{8} + q^{9} + q^{12} - 6q^{13} + q^{14} - q^{16} + 2q^{17} + q^{18} + 8q^{19} + O(q^{20}) \)

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.