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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 41400.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41400.bb1 | 41400bj2 | \([0, 0, 0, -116712075, -485311860250]\) | \(7536914291382802562/17961229575\) | \(418999563525600000000\) | \([2]\) | \(4055040\) | \(3.1984\) | |
| 41400.bb2 | 41400bj1 | \([0, 0, 0, -7209075, -7769277250]\) | \(-3552342505518244/179863605135\) | \(-2097929090294640000000\) | \([2]\) | \(2027520\) | \(2.8519\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41400.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 41400.bb do not have complex multiplication.Modular form 41400.2.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 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.
