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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 5850.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5850.bg1 | 5850bc1 | \([1, -1, 1, -27305, 1743447]\) | \(-8538302475/26\) | \(-6855468750\) | \([]\) | \(12960\) | \(1.1146\) | \(\Gamma_0(N)\)-optimal |
| 5850.bg2 | 5850bc2 | \([1, -1, 1, -17930, 2949697]\) | \(-3316275/17576\) | \(-3378402421875000\) | \([]\) | \(38880\) | \(1.6639\) |
Rank
sage: E.rank()
The elliptic curves in class 5850.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 5850.bg do not have complex multiplication.Modular form 5850.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
