Properties

Label 71058h
Number of curves 2
Conductor 71058
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("71058.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 71058h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71058.h2 71058h1 [1, 1, 1, -397, -3709] [2] 71040 \(\Gamma_0(N)\)-optimal
71058.h1 71058h2 [1, 1, 1, -6637, -210877] [2] 142080  

Rank

sage: E.rank()
 

The elliptic curves in class 71058h have rank \(0\).

Modular form 71058.2.a.h

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} + 4q^{7} + q^{8} + q^{9} + 2q^{10} + 4q^{11} - q^{12} - q^{13} + 4q^{14} - 2q^{15} + q^{16} + q^{18} - 8q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.