Properties

Label 3520u
Number of curves 4
Conductor 3520
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3520.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3520u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3520.d4 3520u1 [0, 1, 0, -181, -981] [2] 1152 \(\Gamma_0(N)\)-optimal
3520.d3 3520u2 [0, 1, 0, -401, 1615] [2] 2304  
3520.d2 3520u3 [0, 1, 0, -1781, 27979] [2] 3456  
3520.d1 3520u4 [0, 1, 0, -28401, 1832815] [2] 6912  

Rank

sage: E.rank()
 

The elliptic curves in class 3520u have rank \(0\).

Modular form 3520.2.a.d

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - q^{5} + 4q^{7} + q^{9} - q^{11} + 4q^{13} + 2q^{15} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.