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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 277350bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277350.bu2 | 277350bu1 | \([1, 0, 1, 3874, -33352]\) | \(222641831/145800\) | \(-4212253125000\) | \([]\) | \(580608\) | \(1.1113\) | \(\Gamma_0(N)\)-optimal |
277350.bu1 | 277350bu2 | \([1, 0, 1, -44501, 4223648]\) | \(-337335507529/72000000\) | \(-2080125000000000\) | \([]\) | \(1741824\) | \(1.6606\) |
Rank
sage: E.rank()
The elliptic curves in class 277350bu have rank \(1\).
Complex multiplication
The elliptic curves in class 277350bu do not have complex multiplication.Modular form 277350.2.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 Cremona 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 Cremona labels.