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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 22848.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22848.br1 | 22848v1 | \([0, 1, 0, -1349, -19509]\) | \(265327034368/297381\) | \(304518144\) | \([2]\) | \(11520\) | \(0.54191\) | \(\Gamma_0(N)\)-optimal |
| 22848.br2 | 22848v2 | \([0, 1, 0, -1009, -29233]\) | \(-6940769488/18000297\) | \(-294916866048\) | \([2]\) | \(23040\) | \(0.88849\) |
Rank
sage: E.rank()
The elliptic curves in class 22848.br have rank \(0\).
Complex multiplication
The elliptic curves in class 22848.br do not have complex multiplication.Modular form 22848.2.a.br
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 LMFDB 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 LMFDB labels.
