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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 35574.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35574.u1 | 35574bk4 | \([1, 0, 1, -2087132, -1160747920]\) | \(4824238966273/66\) | \(13755877085874\) | \([2]\) | \(552960\) | \(2.0770\) | |
| 35574.u2 | 35574bk2 | \([1, 0, 1, -130562, -18111040]\) | \(1180932193/4356\) | \(907887887667684\) | \([2, 2]\) | \(276480\) | \(1.7304\) | |
| 35574.u3 | 35574bk3 | \([1, 0, 1, -71272, -34617376]\) | \(-192100033/2371842\) | \(-494344954835053938\) | \([2]\) | \(552960\) | \(2.0770\) | |
| 35574.u4 | 35574bk1 | \([1, 0, 1, -11982, 7984]\) | \(912673/528\) | \(110047016686992\) | \([2]\) | \(138240\) | \(1.3838\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35574.u have rank \(0\).
Complex multiplication
The elliptic curves in class 35574.u do not have complex multiplication.Modular form 35574.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
