Properties

Label 17661g
Number of curves 2
Conductor 17661
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17661.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17661g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17661.c2 17661g1 [1, 0, 0, -438, 76659] [2] 26880 \(\Gamma_0(N)\)-optimal
17661.c1 17661g2 [1, 0, 0, -29873, 1966386] [2] 53760  

Rank

sage: E.rank()
 

The elliptic curves in class 17661g have rank \(1\).

Modular form 17661.2.a.c

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.