Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("71058.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 71058k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71058.j2 71058k1 [1, 0, 0, -5692, 164816] [3] 85632 \(\Gamma_0(N)\)-optimal
71058.j1 71058k2 [1, 0, 0, -7072, 78524] [] 256896  

Rank

sage: E.rank()
 

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

Modular form 71058.2.a.j

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - 3q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - 3q^{10} + 6q^{11} + q^{12} + q^{13} - q^{14} - 3q^{15} + q^{16} - 3q^{17} + q^{18} + 2q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.