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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 10710be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10710.bf2 | 10710be1 | \([1, -1, 1, 19822, -7742419]\) | \(1181569139409959/36161310937500\) | \(-26361595673437500\) | \([2]\) | \(122880\) | \(1.8309\) | \(\Gamma_0(N)\)-optimal |
| 10710.bf1 | 10710be2 | \([1, -1, 1, -486428, -124382419]\) | \(17460273607244690041/918397653311250\) | \(669511889263901250\) | \([2]\) | \(245760\) | \(2.1775\) |
Rank
sage: E.rank()
The elliptic curves in class 10710be have rank \(0\).
Complex multiplication
The elliptic curves in class 10710be do not have complex multiplication.Modular form 10710.2.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.
