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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 67760bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67760.n2 | 67760bq1 | \([0, -1, 0, -126936, -17947664]\) | \(-456390127585249/17983078400\) | \(-8912701384294400\) | \([]\) | \(580608\) | \(1.8293\) | \(\Gamma_0(N)\)-optimal |
| 67760.n1 | 67760bq2 | \([0, -1, 0, -10377176, -12863233040]\) | \(-249353795628717731809/14000000\) | \(-6938624000000\) | \([]\) | \(1741824\) | \(2.3786\) |
Rank
sage: E.rank()
The elliptic curves in class 67760bq have rank \(0\).
Complex multiplication
The elliptic curves in class 67760bq do not have complex multiplication.Modular form 67760.2.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.
