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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 92400do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.c2 | 92400do1 | \([0, -1, 0, 10352, -423488]\) | \(1197993859655/1437603552\) | \(-147210603724800\) | \([]\) | \(288000\) | \(1.4048\) | \(\Gamma_0(N)\)-optimal |
| 92400.c1 | 92400do2 | \([0, -1, 0, -900208, 329998912]\) | \(-2016939204025/6764142\) | \(-270565680000000000\) | \([]\) | \(1440000\) | \(2.2095\) |
Rank
sage: E.rank()
The elliptic curves in class 92400do have rank \(0\).
Complex multiplication
The elliptic curves in class 92400do do not have complex multiplication.Modular form 92400.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
