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SageMath
E = EllipticCurve("hh1")
E.isogeny_class()
Elliptic curves in class 388416hh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388416.hh1 | 388416hh1 | \([0, 1, 0, -389957, 93508155]\) | \(265327034368/297381\) | \(7350327712551936\) | \([2]\) | \(3317760\) | \(1.9585\) | \(\Gamma_0(N)\)-optimal |
| 388416.hh2 | 388416hh2 | \([0, 1, 0, -291697, 141871727]\) | \(-6940769488/18000297\) | \(-7118576203497357312\) | \([2]\) | \(6635520\) | \(2.3051\) |
Rank
sage: E.rank()
The elliptic curves in class 388416hh have rank \(1\).
Complex multiplication
The elliptic curves in class 388416hh do not have complex multiplication.Modular form 388416.2.a.hh
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.
