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Properties

Label 30926f
Number of curves 6
Conductor 30926
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("30926.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30926f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30926.a5 30926f1 [1, 0, 1, -1151, -30498] [2] 33120 \(\Gamma_0(N)\)-optimal
30926.a4 30926f2 [1, 0, 1, -23241, -1364734] [2] 66240  
30926.a6 30926f3 [1, 0, 1, 9894, 636620] [2] 99360  
30926.a3 30926f4 [1, 0, 1, -78466, 6927852] [2] 198720  
30926.a2 30926f5 [1, 0, 1, -376681, 89208684] [2] 298080  
30926.a1 30926f6 [1, 0, 1, -6031721, 5701270380] [2] 596160  

Rank

sage: E.rank()
 

The elliptic curves in class 30926f have rank \(1\).

Modular form 30926.2.a.a

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.