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Properties

Label 786.f
Number of curves 2
Conductor 786
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("786.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 786.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
786.f1 786f2 [1, 0, 1, -145, -580] [] 456  
786.f2 786f1 [1, 0, 1, -40, 92] [3] 152 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 786.f have rank \(0\).

Modular form 786.2.a.f

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.