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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 2800u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2800.x2 | 2800u1 | \([0, 1, 0, 72, -172]\) | \(397535/392\) | \(-40140800\) | \([]\) | \(576\) | \(0.14598\) | \(\Gamma_0(N)\)-optimal |
| 2800.x1 | 2800u2 | \([0, 1, 0, -728, 10388]\) | \(-417267265/235298\) | \(-24094515200\) | \([]\) | \(1728\) | \(0.69528\) |
Rank
sage: E.rank()
The elliptic curves in class 2800u have rank \(1\).
Complex multiplication
The elliptic curves in class 2800u do not have complex multiplication.Modular form 2800.2.a.u
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.
