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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 165886.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
165886.be1 | 165886k2 | \([1, -1, 1, -2777669367, -56346064121513]\) | \(98191033604529537629349729/10906239337336\) | \(263250104535461976184\) | \([]\) | \(124467840\) | \(3.7873\) | |
165886.be2 | 165886k1 | \([1, -1, 1, -5592927, 4687786567]\) | \(801581275315909089/70810888830976\) | \(1709202715109012537344\) | \([]\) | \(17781120\) | \(2.8144\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 165886.be have rank \(1\).
Complex multiplication
The elliptic curves in class 165886.be do not have complex multiplication.Modular form 165886.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.