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Properties

Label 258f
Number of curves 2
Conductor 258
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("258.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 258f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
258.f2 258f1 [1, 0, 0, 159, 1737] [7] 168 \(\Gamma_0(N)\)-optimal
258.f1 258f2 [1, 0, 0, -59901, -5648523] [] 1176  

Rank

sage: E.rank()
 

The elliptic curves in class 258f have rank \(0\).

Modular form 258.2.a.f

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

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.