Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("525.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 525d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
525.b1 525d1 [1, 0, 0, -18, 27] [2] 48 \(\Gamma_0(N)\)-optimal
525.b2 525d2 [1, 0, 0, 7, 102] [2] 96  

Rank

sage: E.rank()
 

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

Modular form 525.2.a.b

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.