Properties

Label 58989.n
Number of curves 6
Conductor 58989
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("58989.n1")
sage: E.isogeny_class()

Elliptic curves in class 58989.n

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
58989.n1 58989a6 [1, 1, 0, -2202314, -1258878483] 2 599040  
58989.n2 58989a4 [1, 1, 0, -137699, -19696560] 4 299520  
58989.n3 58989a3 [1, 1, 0, -109609, 13837282] 2 299520  
58989.n4 58989a5 [1, 1, 0, -95564, -31924137] 2 599040  
58989.n5 58989a2 [1, 1, 0, -11294, -103785] 4 149760  
58989.n6 58989a1 [1, 1, 0, 2751, -11088] 2 74880 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 58989.n have rank \(1\).

Modular form 58989.2.a.n

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.