Properties

Label 786.d
Number of curves 4
Conductor 786
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("786.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 786.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
786.d1 786e3 [1, 1, 0, -5589, 158517] [2] 576  
786.d2 786e2 [1, 1, 0, -349, 2365] [2, 2] 288  
786.d3 786e4 [1, 1, 0, -229, 4165] [2] 576  
786.d4 786e1 [1, 1, 0, -29, -3] [2] 144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 786.2.a.d

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.