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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 337953be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
337953.be2 | 337953be1 | \([0, -1, 1, -2154203, -1311209824]\) | \(-5304438784000/497763387\) | \(-103745029839702001443\) | \([]\) | \(7776000\) | \(2.5828\) | \(\Gamma_0(N)\)-optimal |
337953.be1 | 337953be2 | \([0, -1, 1, -178245503, -915899486503]\) | \(-3004935183806464000/2037123\) | \(-424582024194043947\) | \([]\) | \(23328000\) | \(3.1321\) |
Rank
sage: E.rank()
The elliptic curves in class 337953be have rank \(0\).
Complex multiplication
The elliptic curves in class 337953be do not have complex multiplication.Modular form 337953.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.