Properties

Label 490k
Number of curves 2
Conductor 490
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("490.e1")
sage: E.isogeny_class()

Elliptic curves in class 490k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
490.e1 490k1 [1, -1, 1, -132, -549] 1 120 \(\Gamma_0(N)\)-optimal
490.e2 490k2 [1, -1, 1, 918, 5289] 7 840  

Rank

sage: E.rank()

The elliptic curves in class 490k have rank \(0\).

Modular form 490.2.a.e

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

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.