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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 5760.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5760.br1 | 5760bo2 | \([0, 0, 0, -372, 1424]\) | \(953312/405\) | \(2418647040\) | \([2]\) | \(2048\) | \(0.49721\) | |
| 5760.br2 | 5760bo1 | \([0, 0, 0, 78, 164]\) | \(281216/225\) | \(-41990400\) | \([2]\) | \(1024\) | \(0.15064\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5760.br have rank \(0\).
Complex multiplication
The elliptic curves in class 5760.br do not have complex multiplication.Modular form 5760.2.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.
