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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 266616bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 266616.bt2 | 266616bt1 | \([0, 0, 0, -12532539, 17076749510]\) | \(1969910093092/7889\) | \(871799181871113216\) | \([2]\) | \(6082560\) | \(2.6538\) | \(\Gamma_0(N)\)-optimal |
| 266616.bt1 | 266616bt2 | \([0, 0, 0, -12722979, 16530986558]\) | \(1030541881826/62236321\) | \(13755247491562424322048\) | \([2]\) | \(12165120\) | \(3.0004\) |
Rank
sage: E.rank()
The elliptic curves in class 266616bt have rank \(1\).
Complex multiplication
The elliptic curves in class 266616bt do not have complex multiplication.Modular form 266616.2.a.bt
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
