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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 59840.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59840.bg1 | 59840bi1 | \([0, 1, 0, -1248225, -537185377]\) | \(-820470116876114809/148618250\) | \(-38959382528000\) | \([]\) | \(663552\) | \(2.0029\) | \(\Gamma_0(N)\)-optimal |
| 59840.bg2 | 59840bi2 | \([0, 1, 0, -1079585, -687352225]\) | \(-530829093701949769/470570890625000\) | \(-123357335552000000000\) | \([]\) | \(1990656\) | \(2.5522\) |
Rank
sage: E.rank()
The elliptic curves in class 59840.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 59840.bg do not have complex multiplication.Modular form 59840.2.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.
