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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 160446u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160446.ba1 | 160446u1 | \([1, 1, 1, -2312373, 1307230299]\) | \(771864882375147625/29358565696512\) | \(52010490003878495232\) | \([2]\) | \(4096000\) | \(2.5513\) | \(\Gamma_0(N)\)-optimal |
| 160446.ba2 | 160446u2 | \([1, 1, 1, 959467, 4713870107]\) | \(55138849409108375/5449537181735712\) | \(-9654187539212899686432\) | \([2]\) | \(8192000\) | \(2.8979\) |
Rank
sage: E.rank()
The elliptic curves in class 160446u have rank \(1\).
Complex multiplication
The elliptic curves in class 160446u do not have complex multiplication.Modular form 160446.2.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.
