Properties

Label 141120.dl
Number of curves 4
Conductor 141120
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("141120.dl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120.dl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.dl1 141120lv4 [0, 0, 0, -3175788, -2178181712] [2] 3145728  
141120.dl2 141120lv2 [0, 0, 0, -212268, -29037008] [2, 2] 1572864  
141120.dl3 141120lv1 [0, 0, 0, -71148, 6920368] [2] 786432 \(\Gamma_0(N)\)-optimal
141120.dl4 141120lv3 [0, 0, 0, 493332, -181164368] [2] 3145728  

Rank

sage: E.rank()
 

The elliptic curves in class 141120.dl have rank \(1\).

Modular form 141120.2.a.dl

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.