Properties

Label 71058.n
Number of curves 2
Conductor 71058
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("71058.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 71058.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71058.n1 71058j2 [1, 0, 0, -10797, 430917] [2] 86016  
71058.n2 71058j1 [1, 0, 0, -657, 7065] [2] 43008 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 71058.n have rank \(1\).

Modular form 71058.2.a.n

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} - 2q^{7} + q^{8} + q^{9} + 2q^{10} + q^{12} - q^{13} - 2q^{14} + 2q^{15} + q^{16} + 4q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.