Properties

Label 480240do
Number of curves 2
Conductor 480240
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("480240.do1")
sage: E.isogeny_class()

Elliptic curves in class 480240do

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
480240.do1 480240do1 [0, 0, 0, -53787, 4801034] 2 884736 \(\Gamma_0(N)\)-optimal
480240.do2 480240do2 [0, 0, 0, -50187, 5471354] 2 1769472  

Rank

sage: E.rank()

The elliptic curves in class 480240do have rank \(0\).

Modular form 480240.2.a.do

sage: E.q_eigenform(10)
\( q + q^{5} + 2q^{11} + 2q^{13} + 4q^{17} + O(q^{20}) \)

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.