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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 418950be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.be1 | 418950be1 | \([1, -1, 0, -1053117, -415638959]\) | \(96386901625/18468\) | \(24748886291062500\) | \([2]\) | \(6635520\) | \(2.1463\) | \(\Gamma_0(N)\)-optimal |
418950.be2 | 418950be2 | \([1, -1, 0, -942867, -506154209]\) | \(-69173457625/42633378\) | \(-57132804002917781250\) | \([2]\) | \(13271040\) | \(2.4929\) |
Rank
sage: E.rank()
The elliptic curves in class 418950be have rank \(1\).
Complex multiplication
The elliptic curves in class 418950be do not have complex multiplication.Modular form 418950.2.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.