Properties

Label 528.i
Number of curves 4
Conductor 528
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("528.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 528.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
528.i1 528d3 [0, 1, 0, -472, -4108] [2] 128  
528.i2 528d2 [0, 1, 0, -32, -60] [2, 2] 64  
528.i3 528d1 [0, 1, 0, -12, 12] [2] 32 \(\Gamma_0(N)\)-optimal
528.i4 528d4 [0, 1, 0, 88, -300] [2] 128  

Rank

sage: E.rank()
 

The elliptic curves in class 528.i have rank \(0\).

Modular form 528.2.a.i

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} + q^{9} - q^{11} + 2q^{13} + 2q^{15} + 6q^{17} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.