Properties

Label 525c
Number of curves 2
Conductor 525
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("525.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 525c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
525.c1 525c1 [1, 1, 0, -450, 3375] [2] 240 \(\Gamma_0(N)\)-optimal
525.c2 525c2 [1, 1, 0, 175, 12750] [2] 480  

Rank

sage: E.rank()
 

The elliptic curves in class 525c have rank \(1\).

Modular form 525.2.a.c

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} - q^{6} + q^{7} - 3q^{8} + q^{9} - 6q^{11} + q^{12} + 2q^{13} + q^{14} - q^{16} - 4q^{17} + q^{18} - 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.