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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 289800.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 289800.bf1 | 289800bf2 | \([0, 0, 0, -3817875, -418635250]\) | \(263822189935250/149429406721\) | \(3485889199987488000000\) | \([2]\) | \(13271040\) | \(2.8235\) | |
| 289800.bf2 | 289800bf1 | \([0, 0, 0, 943125, -52038250]\) | \(7953970437500/4703287687\) | \(-54859147581168000000\) | \([2]\) | \(6635520\) | \(2.4770\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 289800.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 289800.bf do not have complex multiplication.Modular form 289800.2.a.bf
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.
