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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 108900cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 108900.dh2 | 108900cd1 | \([0, 0, 0, -2105400, 1366770625]\) | \(-3196715008/649539\) | \(-209714703279072750000\) | \([2]\) | \(3686400\) | \(2.6218\) | \(\Gamma_0(N)\)-optimal |
| 108900.dh1 | 108900cd2 | \([0, 0, 0, -35183775, 80324851750]\) | \(932410994128/29403\) | \(151892130770028000000\) | \([2]\) | \(7372800\) | \(2.9683\) |
Rank
sage: E.rank()
The elliptic curves in class 108900cd have rank \(0\).
Complex multiplication
The elliptic curves in class 108900cd do not have complex multiplication.Modular form 108900.2.a.cd
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.
