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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 9200.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9200.bh1 | 9200bi2 | \([0, -1, 0, -1108, 14412]\) | \(941054800/12167\) | \(1946720000\) | \([]\) | \(6048\) | \(0.59071\) | |
| 9200.bh2 | 9200bi1 | \([0, -1, 0, -108, -388]\) | \(878800/23\) | \(3680000\) | \([]\) | \(2016\) | \(0.041406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9200.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 9200.bh do not have complex multiplication.Modular form 9200.2.a.bh
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
