Properties

Label 17787.w
Number of curves 6
Conductor 17787
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17787.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17787.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17787.w1 17787o5 [1, 0, 1, -26793275, -53383219837] [2] 921600  
17787.w2 17787o3 [1, 0, 1, -1683960, -824401679] [2, 2] 460800  
17787.w3 17787o2 [1, 0, 1, -231355, 23919641] [2, 2] 230400  
17787.w4 17787o1 [1, 0, 1, -201710, 34840859] [2] 115200 \(\Gamma_0(N)\)-optimal
17787.w5 17787o6 [1, 0, 1, 183675, -2552337581] [2] 921600  
17787.w6 17787o4 [1, 0, 1, 746930, 173401589] [2] 460800  

Rank

sage: E.rank()
 

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

Modular form 17787.2.a.w

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} + 2q^{5} + q^{6} - 3q^{8} + q^{9} + 2q^{10} - q^{12} + 6q^{13} + 2q^{15} - q^{16} + 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.