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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 11760.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11760.br1 | 11760ce3 | \([0, 1, 0, -88216, -10113580]\) | \(157551496201/13125\) | \(6324810240000\) | \([2]\) | \(49152\) | \(1.5001\) | |
| 11760.br2 | 11760ce2 | \([0, 1, 0, -5896, -136396]\) | \(47045881/11025\) | \(5312840601600\) | \([2, 2]\) | \(24576\) | \(1.1536\) | |
| 11760.br3 | 11760ce1 | \([0, 1, 0, -1976, 31380]\) | \(1771561/105\) | \(50598481920\) | \([2]\) | \(12288\) | \(0.80699\) | \(\Gamma_0(N)\)-optimal |
| 11760.br4 | 11760ce4 | \([0, 1, 0, 13704, -834156]\) | \(590589719/972405\) | \(-468592541061120\) | \([2]\) | \(49152\) | \(1.5001\) |
Rank
sage: E.rank()
The elliptic curves in class 11760.br have rank \(0\).
Complex multiplication
The elliptic curves in class 11760.br do not have complex multiplication.Modular form 11760.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
