Properties

Label 17238f
Number of curves 6
Conductor 17238
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17238.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17238f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17238.e5 17238f1 [1, 0, 1, -5750, 155144] [2] 36864 \(\Gamma_0(N)\)-optimal
17238.e4 17238f2 [1, 0, 1, -19270, -850744] [2, 2] 73728  
17238.e2 17238f3 [1, 0, 1, -293050, -61082344] [2, 2] 147456  
17238.e6 17238f4 [1, 0, 1, 38190, -4941896] [2] 147456  
17238.e1 17238f5 [1, 0, 1, -4688740, -3908190232] [2] 294912  
17238.e3 17238f6 [1, 0, 1, -277840, -67701736] [2] 294912  

Rank

sage: E.rank()
 

The elliptic curves in class 17238f have rank \(1\).

Modular form 17238.2.a.e

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.