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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 86490.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86490.bu1 | 86490cf2 | \([1, -1, 1, -17406293, -9789531843]\) | \(901456690969801/457629750000\) | \(296081955904220007750000\) | \([2]\) | \(14745600\) | \(3.1962\) | |
86490.bu2 | 86490cf1 | \([1, -1, 1, 4043227, -1183984419]\) | \(11298232190519/7472736000\) | \(-4834786835505946464000\) | \([2]\) | \(7372800\) | \(2.8496\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86490.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 86490.bu do not have complex multiplication.Modular form 86490.2.a.bu
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.