Properties

Label 17.a
Number of curves 4
Conductor 17
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("17.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17.a1 17a3 [1, -1, 1, -91, -310] [2] 4  
17.a2 17a2 [1, -1, 1, -6, -4] [2, 2] 2  
17.a3 17a1 [1, -1, 1, -1, -14] [4] 1 \(\Gamma_0(N)\)-optimal
17.a4 17a4 [1, -1, 1, -1, 0] [4] 4  

Rank

sage: E.rank()
 

The elliptic curves in class 17.a have rank \(0\).

Modular form 17.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.