Properties

Label 71630x
Number of curves 2
Conductor 71630
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("71630.v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 71630x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71630.v2 71630x1 [1, -1, 1, -265716552, 1667217712779] [7] 26254592 \(\Gamma_0(N)\)-optimal
71630.v1 71630x2 [1, -1, 1, -6564370452, -204561760368501] [] 183782144  

Rank

sage: E.rank()
 

The elliptic curves in class 71630x have rank \(1\).

Modular form 71630.2.a.v

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

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.