Properties

Label 528g
Number of curves 4
Conductor 528
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("528.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 528g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
528.d3 528g1 [0, -1, 0, -88, -272] [2] 96 \(\Gamma_0(N)\)-optimal
528.d4 528g2 [0, -1, 0, 72, -1296] [2] 192  
528.d1 528g3 [0, -1, 0, -1288, 18160] [2] 288  
528.d2 528g4 [0, -1, 0, -648, 35568] [2] 576  

Rank

sage: E.rank()
 

The elliptic curves in class 528g have rank \(1\).

Modular form 528.2.a.d

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.