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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 56784be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56784.r2 | 56784be1 | \([0, -1, 0, -1408, 2560]\) | \(2640625/1512\) | \(176882614272\) | \([]\) | \(48384\) | \(0.84794\) | \(\Gamma_0(N)\)-optimal |
| 56784.r1 | 56784be2 | \([0, -1, 0, -82528, 9152896]\) | \(531373116625/2058\) | \(240756891648\) | \([]\) | \(145152\) | \(1.3972\) |
Rank
sage: E.rank()
The elliptic curves in class 56784be have rank \(2\).
Complex multiplication
The elliptic curves in class 56784be do not have complex multiplication.Modular form 56784.2.a.be
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
