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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 160560u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160560.j2 | 160560u1 | \([0, 0, 0, -979203, 415699202]\) | \(-34773983355859201/4877010000000\) | \(-14562673827840000000\) | \([]\) | \(3838464\) | \(2.4084\) | \(\Gamma_0(N)\)-optimal |
| 160560.j1 | 160560u2 | \([0, 0, 0, -32580003, -103971057118]\) | \(-1280824409818832580001/822726139895701410\) | \(-2456647090110326079037440\) | \([]\) | \(26869248\) | \(3.3814\) |
Rank
sage: E.rank()
The elliptic curves in class 160560u have rank \(0\).
Complex multiplication
The elliptic curves in class 160560u do not have complex multiplication.Modular form 160560.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
