Properties

Label 141570.de
Number of curves $6$
Conductor $141570$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("141570.de1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141570.de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141570.de1 141570bq6 [1, -1, 1, -9817358, -11837226189] [2] 5242880  
141570.de2 141570bq3 [1, -1, 1, -920228, 339736587] [2] 2621440  
141570.de3 141570bq4 [1, -1, 1, -615308, -183750069] [2, 2] 2621440  
141570.de4 141570bq5 [1, -1, 1, -125258, -468763149] [2] 5242880  
141570.de5 141570bq2 [1, -1, 1, -70808, 2686731] [2, 2] 1310720  
141570.de6 141570bq1 [1, -1, 1, 16312, 317067] [2] 655360 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141570.de have rank \(2\).

Modular form 141570.2.a.de

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} - q^{13} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.