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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 9900r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9900.g2 | 9900r1 | \([0, 0, 0, -17400, -1026875]\) | \(-3196715008/649539\) | \(-118378482750000\) | \([2]\) | \(30720\) | \(1.4228\) | \(\Gamma_0(N)\)-optimal |
| 9900.g1 | 9900r2 | \([0, 0, 0, -290775, -60349250]\) | \(932410994128/29403\) | \(85739148000000\) | \([2]\) | \(61440\) | \(1.7694\) |
Rank
sage: E.rank()
The elliptic curves in class 9900r have rank \(0\).
Complex multiplication
The elliptic curves in class 9900r do not have complex multiplication.Modular form 9900.2.a.r
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.
