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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 283920.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.r1 | 283920r1 | \([0, -1, 0, -6239047416, 189674320253040]\) | \(1358496453776544375572161/78807337984327680\) | \(1558069117947063110750699520\) | \([2]\) | \(298045440\) | \(4.2808\) | \(\Gamma_0(N)\)-optimal |
| 283920.r2 | 283920r2 | \([0, -1, 0, -5879090936, 212522629812336]\) | \(-1136669439536177967564481/329089027143166617600\) | \(-6506290700353048241484752486400\) | \([2]\) | \(596090880\) | \(4.6274\) |
Rank
sage: E.rank()
The elliptic curves in class 283920.r have rank \(0\).
Complex multiplication
The elliptic curves in class 283920.r do not have complex multiplication.Modular form 283920.2.a.r
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.
