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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 64896be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64896.be2 | 64896be1 | \([0, 1, 0, 282, 3186]\) | \(4000/9\) | \(-5560483968\) | \([2]\) | \(30720\) | \(0.55403\) | \(\Gamma_0(N)\)-optimal |
| 64896.be1 | 64896be2 | \([0, 1, 0, -2253, 33099]\) | \(16000/3\) | \(237247315968\) | \([2]\) | \(61440\) | \(0.90060\) |
Rank
sage: E.rank()
The elliptic curves in class 64896be have rank \(1\).
Complex multiplication
The elliptic curves in class 64896be do not have complex multiplication.Modular form 64896.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
