Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("528.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 528f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
528.a3 528f1 [0, -1, 0, -720, -5184] [2] 480 \(\Gamma_0(N)\)-optimal
528.a4 528f2 [0, -1, 0, 1840, -35904] [2] 960  
528.a1 528f3 [0, -1, 0, -161040, 24927936] [2] 2400  
528.a2 528f4 [0, -1, 0, -160880, 24979776] [2] 4800  

Rank

sage: E.rank()
 

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

Modular form 528.2.a.a

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.