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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 206400.do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206400.do1 | 206400io2 | \([0, -1, 0, -4536833, 3029121537]\) | \(20170293914861/3938458752\) | \(2016490881024000000000\) | \([2]\) | \(10321920\) | \(2.8047\) | |
| 206400.do2 | 206400io1 | \([0, -1, 0, 583167, 279681537]\) | \(42838260499/90882048\) | \(-46531608576000000000\) | \([2]\) | \(5160960\) | \(2.4582\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206400.do have rank \(1\).
Complex multiplication
The elliptic curves in class 206400.do do not have complex multiplication.Modular form 206400.2.a.do
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.
