Properties

Label 17787h
Number of curves 6
Conductor 17787
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("17787.s1")
sage: E.isogeny_class()

Elliptic curves in class 17787h

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
17787.s6 17787h1 [1, 1, 0, 5806, -35097] 2 30720 \(\Gamma_0(N)\)-optimal
17787.s5 17787h2 [1, 1, 0, -23839, -313760] 4 61440  
17787.s2 17787h3 [1, 1, 0, -290644, -60344885] 4 122880  
17787.s3 17787h4 [1, 1, 0, -231354, 42475833] 2 122880  
17787.s1 17787h5 [1, 1, 0, -4648459, -3859488002] 2 245760  
17787.s4 17787h6 [1, 1, 0, -201709, -97857668] 2 245760  

Rank

sage: E.rank()

The elliptic curves in class 17787h have rank \(1\).

Modular form 17787.2.a.s

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.