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Properties

Label 290145f
Number of curves 2
Conductor 290145
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("290145.f1")
sage: E.isogeny_class()

Elliptic curves in class 290145f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
290145.f1 290145f1 [1, 1, 1, -314131, 67630928] 2 1451520 \(\Gamma_0(N)\)-optimal
290145.f2 290145f2 [1, 1, 1, -293106, 77100588] 2 2903040  

Rank

sage: E.rank()

The elliptic curves in class 290145f have rank \(1\).

Modular form 290145.2.a.f

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.