Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("528.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 528b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
528.b4 528b1 [0, -1, 0, 1, -6] [2] 48 \(\Gamma_0(N)\)-optimal
528.b3 528b2 [0, -1, 0, -44, -96] [2, 2] 96  
528.b1 528b3 [0, -1, 0, -704, -6960] [2] 192  
528.b2 528b4 [0, -1, 0, -104, 288] [4] 192  

Rank

sage: E.rank()
 

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

Modular form 528.2.a.b

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{5} - 4q^{7} + q^{9} + q^{11} + 6q^{13} + 2q^{15} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.