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SageMath
sage: E = EllipticCurve("f1")
sage: E.isogeny_class()
Elliptic curves in class 97020f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 97020.d3 | 97020f1 | [0, 0, 0, -50568, 353633] | [2] | 497664 | \(\Gamma_0(N)\)-optimal |
| 97020.d4 | 97020f2 | [0, 0, 0, 201537, 2824262] | [2] | 995328 | |
| 97020.d1 | 97020f3 | [0, 0, 0, -2931768, 1932150213] | [2] | 1492992 | |
| 97020.d2 | 97020f4 | [0, 0, 0, -2885463, 1996134462] | [2] | 2985984 |
Rank
sage: E.rank()
The elliptic curves in class 97020f have rank \(1\).
Complex multiplication
The elliptic curves in class 97020f do not have complex multiplication.Modular form 97020.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
