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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 388416n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388416.n2 | 388416n1 | \([0, -1, 0, 2135903, 1764959521]\) | \(49218965184023/89996344704\) | \(-1970427581175636688896\) | \([]\) | \(17418240\) | \(2.7708\) | \(\Gamma_0(N)\)-optimal |
| 388416.n1 | 388416n2 | \([0, -1, 0, -20336737, -65450706719]\) | \(-42484640023394137/59954864062464\) | \(-1312683511345592596955136\) | \([]\) | \(52254720\) | \(3.3201\) |
Rank
sage: E.rank()
The elliptic curves in class 388416n have rank \(1\).
Complex multiplication
The elliptic curves in class 388416n do not have complex multiplication.Modular form 388416.2.a.n
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.
