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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 38962be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38962.be2 | 38962be1 | \([1, 0, 0, -37694, 2461592]\) | \(3343374301177/453439756\) | \(803296187579116\) | \([]\) | \(195840\) | \(1.5872\) | \(\Gamma_0(N)\)-optimal |
38962.be1 | 38962be2 | \([1, 0, 0, -2945929, 1945927897]\) | \(1596005697643892137/5553856\) | \(9838994689216\) | \([]\) | \(587520\) | \(2.1365\) |
Rank
sage: E.rank()
The elliptic curves in class 38962be have rank \(0\).
Complex multiplication
The elliptic curves in class 38962be do not have complex multiplication.Modular form 38962.2.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.