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SageMath
sage: E = EllipticCurve("f1")
sage: E.isogeny_class()
Elliptic curves in class 3630.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 3630.f1 | 3630d5 | [1, 1, 0, -20701287, 36244390329] | [4] | 184320 | |
| 3630.f2 | 3630d3 | [1, 1, 0, -1430827, -657916211] | [2] | 92160 | |
| 3630.f3 | 3630d4 | [1, 1, 0, -1295307, 564555501] | [2, 2] | 92160 | |
| 3630.f4 | 3630d6 | [1, 1, 0, -629807, 1144738401] | [2] | 184320 | |
| 3630.f5 | 3630d2 | [1, 1, 0, -124027, -1641251] | [2, 2] | 46080 | |
| 3630.f6 | 3630d1 | [1, 1, 0, 30853, -185379] | [2] | 23040 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3630.f have rank \(1\).
Complex multiplication
The elliptic curves in class 3630.f do not have complex multiplication.Modular form 3630.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
