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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 57222.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57222.bj1 | 57222bv2 | \([1, -1, 1, -3190181, 1267288341]\) | \(204055591784617/78708537864\) | \(1384978084650849797064\) | \([2]\) | \(3096576\) | \(2.7557\) | |
| 57222.bj2 | 57222bv1 | \([1, -1, 1, -1421501, -637933755]\) | \(18052771191337/444958272\) | \(7829613813547639872\) | \([2]\) | \(1548288\) | \(2.4091\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57222.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 57222.bj do not have complex multiplication.Modular form 57222.2.a.bj
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.
