Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3528.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3528.w1 3528x3 [0, 0, 0, -67179, 6693302] [2] 12288  
3528.w2 3528x2 [0, 0, 0, -5439, 37730] [2, 2] 6144  
3528.w3 3528x1 [0, 0, 0, -3234, -70315] [2] 3072 \(\Gamma_0(N)\)-optimal
3528.w4 3528x4 [0, 0, 0, 21021, 297038] [2] 12288  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3528.2.a.w

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.