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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 424830do
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.do2 | 424830do1 | \([1, 0, 1, -363461103, 2678989207906]\) | \(-9186763300983704416553/47730830553907200\) | \(-27588875269089354212966400\) | \([2]\) | \(212336640\) | \(3.7274\) | \(\Gamma_0(N)\)-optimal* |
424830.do1 | 424830do2 | \([1, 0, 1, -5822609903, 171010750626146]\) | \(37769548376817211811066153/1011738331054080\) | \(584794404297721502760960\) | \([2]\) | \(424673280\) | \(4.0740\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830do have rank \(0\).
Complex multiplication
The elliptic curves in class 424830do do not have complex multiplication.Modular form 424830.2.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 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.