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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 388416q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388416.q1 | 388416q1 | \([0, -1, 0, -3464917, -2539379891]\) | \(-11632923639808/318495051\) | \(-125955215682289975296\) | \([]\) | \(15925248\) | \(2.6381\) | \(\Gamma_0(N)\)-optimal |
| 388416.q2 | 388416q2 | \([0, -1, 0, 15401003, -10253654579]\) | \(1021544365555712/705905647251\) | \(-279164457255086863466496\) | \([]\) | \(47775744\) | \(3.1874\) |
Rank
sage: E.rank()
The elliptic curves in class 388416q have rank \(1\).
Complex multiplication
The elliptic curves in class 388416q do not have complex multiplication.Modular form 388416.2.a.q
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.
