Properties

Label 3528.d
Number of curves $6$
Conductor $3528$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3528.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3528.d1 3528l5 [0, 0, 0, -169491, -26857586] [2] 12288  
3528.d2 3528l4 [0, 0, 0, -28371, 1839166] [2] 6144  
3528.d3 3528l3 [0, 0, 0, -10731, -408170] [2, 2] 6144  
3528.d4 3528l2 [0, 0, 0, -1911, 24010] [2, 2] 3072  
3528.d5 3528l1 [0, 0, 0, 294, 2401] [2] 1536 \(\Gamma_0(N)\)-optimal
3528.d6 3528l6 [0, 0, 0, 6909, -1618274] [2] 12288  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3528.2.a.d

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.