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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 58800.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.br1 | 58800fq1 | \([0, -1, 0, -6533, 76812]\) | \(1048576/525\) | \(15441431250000\) | \([2]\) | \(110592\) | \(1.2235\) | \(\Gamma_0(N)\)-optimal |
| 58800.br2 | 58800fq2 | \([0, -1, 0, 24092, 566812]\) | \(3286064/2205\) | \(-1037664180000000\) | \([2]\) | \(221184\) | \(1.5700\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.br have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.br do not have complex multiplication.Modular form 58800.2.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.
