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Properties

Label 71058.j
Number of curves $2$
Conductor $71058$
CM no
Rank $0$
Graph

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

Elliptic curves in class 71058.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
71058.j1 71058k2 \([1, 0, 0, -7072, 78524]\) \(39115988185876993/19932713929284\) \(19932713929284\) \([]\) \(256896\) \(1.2443\)  
71058.j2 71058k1 \([1, 0, 0, -5692, 164816]\) \(20394973955109313/20464704\) \(20464704\) \([3]\) \(85632\) \(0.69502\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 71058.j do not have complex multiplication.

Modular form 71058.2.a.j

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.