Properties

Label 17457.a
Number of curves 2
Conductor 17457
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17457.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17457.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17457.a1 17457b2 [1, 1, 1, -654913, 202137092] [2] 168960  
17457.a2 17457b1 [1, 1, 1, -12178, 7516934] [2] 84480 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17457.a have rank \(0\).

Modular form 17457.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} - q^{4} + q^{6} + 2q^{7} + 3q^{8} + q^{9} - q^{11} + q^{12} + 2q^{13} - 2q^{14} - q^{16} - q^{18} - 2q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.