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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 117117.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117117.bq1 | 117117bd2 | \([1, -1, 0, -1533726, 487866757]\) | \(249120591156760861/80068829743287\) | \(128239278611635121931\) | \([2]\) | \(3317760\) | \(2.5619\) | |
| 117117.bq2 | 117117bd1 | \([1, -1, 0, 272169, 51923704]\) | \(1392134518764179/1534746617019\) | \(-2458070133523651647\) | \([2]\) | \(1658880\) | \(2.2154\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 117117.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 117117.bq do not have complex multiplication.Modular form 117117.2.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 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.
