Properties

Label 71148.l
Number of curves 2
Conductor 71148
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("71148.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 71148.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71148.l1 71148v2 [0, -1, 0, -73124, -3594072] [2] 518400  
71148.l2 71148v1 [0, -1, 0, 15811, -427986] [2] 259200 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 71148.l have rank \(0\).

Modular form 71148.2.a.l

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

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.