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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 47040.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47040.be1 | 47040ej1 | \([0, -1, 0, -961, 4705]\) | \(1092727/540\) | \(48554311680\) | \([2]\) | \(36864\) | \(0.74359\) | \(\Gamma_0(N)\)-optimal |
| 47040.be2 | 47040ej2 | \([0, -1, 0, 3519, 32481]\) | \(53582633/36450\) | \(-3277416038400\) | \([2]\) | \(73728\) | \(1.0902\) |
Rank
sage: E.rank()
The elliptic curves in class 47040.be have rank \(1\).
Complex multiplication
The elliptic curves in class 47040.be do not have complex multiplication.Modular form 47040.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
