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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 106470bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106470.f2 | 106470bb1 | \([1, -1, 0, 2565135, -253085715]\) | \(18573478391/11022480\) | \(-1107746460072873064080\) | \([]\) | \(5391360\) | \(2.7274\) | \(\Gamma_0(N)\)-optimal |
| 106470.f1 | 106470bb2 | \([1, -1, 0, -32136480, 77596517376]\) | \(-36522255042169/4741632000\) | \(-476528518352336067072000\) | \([]\) | \(16174080\) | \(3.2767\) |
Rank
sage: E.rank()
The elliptic curves in class 106470bb have rank \(0\).
Complex multiplication
The elliptic curves in class 106470bb do not have complex multiplication.Modular form 106470.2.a.bb
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.
