Properties

Label 212160.bl
Number of curves 2
Conductor 212160
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("212160.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 212160.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
212160.bl1 212160dx1 [0, -1, 0, -871681, -309383519] [2] 2949120 \(\Gamma_0(N)\)-optimal
212160.bl2 212160dx2 [0, -1, 0, -134401, -816779615] [2] 5898240  

Rank

sage: E.rank()
 

The elliptic curves in class 212160.bl have rank \(1\).

Modular form 212160.2.a.bl

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + 2q^{7} + q^{9} + q^{13} + q^{15} - q^{17} + 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.