Properties

Label 17787.o
Number of curves 4
Conductor 17787
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17787.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17787.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17787.o1 17787u3 [1, 0, 0, -868722, 311273073] [2] 207360  
17787.o2 17787u2 [1, 0, 0, -68307, 2152800] [2, 2] 103680  
17787.o3 17787u1 [1, 0, 0, -38662, -2904637] [2] 51840 \(\Gamma_0(N)\)-optimal
17787.o4 17787u4 [1, 0, 0, 257788, 16827075] [2] 207360  

Rank

sage: E.rank()
 

The elliptic curves in class 17787.o have rank \(0\).

Modular form 17787.2.a.o

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} - q^{4} + 2q^{5} - q^{6} + 3q^{8} + q^{9} - 2q^{10} - q^{12} - 2q^{13} + 2q^{15} - q^{16} - 2q^{17} - q^{18} + O(q^{20}) \)

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 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.