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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 244398.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
244398.bf1 | 244398bf2 | \([1, 1, 1, -3938416, -3009241519]\) | \(45637459887836881/13417633152\) | \(1986291251932192128\) | \([2]\) | \(15138816\) | \(2.4901\) | |
244398.bf2 | 244398bf1 | \([1, 1, 1, -214256, -59706799]\) | \(-7347774183121/6119866368\) | \(-905959858348081152\) | \([2]\) | \(7569408\) | \(2.1435\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 244398.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 244398.bf do not have complex multiplication.Modular form 244398.2.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.