Properties

Label 3528.v
Number of curves $4$
Conductor $3528$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3528.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3528.v1 3528y4 [0, 0, 0, -1778259, 912726430] [2] 36864  
3528.v2 3528y3 [0, 0, 0, -173019, -3322298] [2] 36864  
3528.v3 3528y2 [0, 0, 0, -111279, 14224210] [2, 2] 18432  
3528.v4 3528y1 [0, 0, 0, -3234, 459277] [2] 9216 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3528.v have rank \(0\).

Complex multiplication

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

Modular form 3528.2.a.v

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

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.