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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 11200bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11200.bd2 | 11200bq1 | \([0, -1, 0, 7167, 193537]\) | \(397535/392\) | \(-40140800000000\) | \([]\) | \(23040\) | \(1.2973\) | \(\Gamma_0(N)\)-optimal |
| 11200.bd1 | 11200bq2 | \([0, -1, 0, -72833, -10606463]\) | \(-417267265/235298\) | \(-24094515200000000\) | \([]\) | \(69120\) | \(1.8466\) |
Rank
sage: E.rank()
The elliptic curves in class 11200bq have rank \(1\).
Complex multiplication
The elliptic curves in class 11200bq do not have complex multiplication.Modular form 11200.2.a.bq
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.
