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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 16830.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16830.bu1 | 16830ch2 | \([1, -1, 1, -1671323, 832063947]\) | \(708234550511150304361/23696640000\) | \(17274850560000\) | \([2]\) | \(225280\) | \(2.0396\) | |
16830.bu2 | 16830ch1 | \([1, -1, 1, -104603, 12982731]\) | \(173629978755828841/1000026931200\) | \(729019632844800\) | \([2]\) | \(112640\) | \(1.6930\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16830.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 16830.bu do not have complex multiplication.Modular form 16830.2.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.