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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 53550.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53550.bn1 | 53550bo2 | \([1, -1, 0, -8478792, 9493043616]\) | \(5918043195362419129/8515734343200\) | \(96999536503012500000\) | \([2]\) | \(2949120\) | \(2.7375\) | |
| 53550.bn2 | 53550bo1 | \([1, -1, 0, -378792, 234743616]\) | \(-527690404915129/1782829440000\) | \(-20307541590000000000\) | \([2]\) | \(1474560\) | \(2.3910\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53550.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 53550.bn do not have complex multiplication.Modular form 53550.2.a.bn
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.
