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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 35322u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35322.v2 | 35322u1 | \([1, 1, 1, 92072, 2504729]\) | \(145116956375/88397568\) | \(-52580934966083328\) | \([2]\) | \(268800\) | \(1.8976\) | \(\Gamma_0(N)\)-optimal |
| 35322.v1 | 35322u2 | \([1, 1, 1, -378888, 19836057]\) | \(10112728515625/5561943408\) | \(3308373649160617968\) | \([2]\) | \(537600\) | \(2.2442\) |
Rank
sage: E.rank()
The elliptic curves in class 35322u have rank \(0\).
Complex multiplication
The elliptic curves in class 35322u do not have complex multiplication.Modular form 35322.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
