Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("786.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 786i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
786.k1 786i1 [1, 1, 1, -71, -259] [2] 288 \(\Gamma_0(N)\)-optimal
786.k2 786i2 [1, 1, 1, -31, -499] [2] 576  

Rank

sage: E.rank()
 

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

Modular form 786.2.a.k

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

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 Cremona 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 Cremona labels.