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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 286650be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.be2 | 286650be1 | \([1, -1, 0, 328683, 8563841]\) | \(108531333/63700\) | \(-2304830492310937500\) | \([2]\) | \(4423680\) | \(2.2129\) | \(\Gamma_0(N)\)-optimal |
| 286650.be1 | 286650be2 | \([1, -1, 0, -1325067, 69752591]\) | \(7111117467/4057690\) | \(146817702360206718750\) | \([2]\) | \(8847360\) | \(2.5594\) |
Rank
sage: E.rank()
The elliptic curves in class 286650be have rank \(0\).
Complex multiplication
The elliptic curves in class 286650be do not have complex multiplication.Modular form 286650.2.a.be
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 Cremona 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 Cremona labels.
