Properties

Label 20181.e
Number of curves 6
Conductor 20181
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("20181.e1")
sage: E.isogeny_class()

Elliptic curves in class 20181.e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
20181.e1 20181d5 [1, 1, 1, -753444, 251410050] 2 122880  
20181.e2 20181d4 [1, 1, 1, -47109, 3910266] 4 61440  
20181.e3 20181d3 [1, 1, 1, -37499, -2793670] 2 61440  
20181.e4 20181d6 [1, 1, 1, -32694, 6366582] 2 122880  
20181.e5 20181d2 [1, 1, 1, -3864, 18216] 4 30720  
20181.e6 20181d1 [1, 1, 1, 941, 2840] 2 15360 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 20181.e have rank \(0\).

Modular form 20181.2.a.e

sage: E.q_eigenform(10)
\( q - q^{2} - q^{3} - q^{4} - 2q^{5} + q^{6} - q^{7} + 3q^{8} + q^{9} + 2q^{10} - 4q^{11} + q^{12} + 2q^{13} + q^{14} + 2q^{15} - q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.