Properties

Label 3528.x
Number of curves $4$
Conductor $3528$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3528.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3528.x1 3528k4 [0, 0, 0, -131859, 18429390] [2] 12288  
3528.x2 3528k3 [0, 0, 0, -26019, -1278018] [2] 12288  
3528.x3 3528k2 [0, 0, 0, -8379, 277830] [2, 2] 6144  
3528.x4 3528k1 [0, 0, 0, 441, 18522] [2] 3072 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3528.x have rank \(1\).

Complex multiplication

The elliptic curves in class 3528.x do not have complex multiplication.

Modular form 3528.2.a.x

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.