Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("528.g1")
sage: E.isogeny_class()

Elliptic curves in class 528.g

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
528.g1 528h3 [0, 1, 0, -2344, -44428] 2 384  
528.g2 528h2 [0, 1, 0, -184, -364] 4 192  
528.g3 528h1 [0, 1, 0, -104, 372] 2 96 \(\Gamma_0(N)\)-optimal
528.g4 528h4 [0, 1, 0, 696, -2124] 4 384  

Rank

sage: E.rank()

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

Modular form 528.2.a.g

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

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 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.