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SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 284592gh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 284592.gh2 | 284592gh1 | \([0, 1, 0, 2227328, 1569964724]\) | \(596183/864\) | \(-1770965910687528124416\) | \([]\) | \(13608000\) | \(2.7627\) | \(\Gamma_0(N)\)-optimal |
| 284592.gh1 | 284592gh2 | \([0, 1, 0, -67497712, 214510236884]\) | \(-16591834777/98304\) | \(-201496565838225422155776\) | \([]\) | \(40824000\) | \(3.3120\) |
Rank
sage: E.rank()
The elliptic curves in class 284592gh have rank \(1\).
Complex multiplication
The elliptic curves in class 284592gh do not have complex multiplication.Modular form 284592.2.a.gh
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
