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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 277350.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277350.bb1 | 277350bb2 | \([1, 0, 1, -14333401, 20885608448]\) | \(262147686417280027/22500\) | \(27951679687500\) | \([2]\) | \(8110080\) | \(2.4664\) | |
277350.bb2 | 277350bb1 | \([1, 0, 1, -895901, 326233448]\) | \(64014401080027/18750000\) | \(23293066406250000\) | \([2]\) | \(4055040\) | \(2.1198\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277350.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 277350.bb do not have complex multiplication.Modular form 277350.2.a.bb
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.