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SageMath
sage: E = EllipticCurve("o1")
sage: E.isogeny_class()
Elliptic curves in class 348726o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 348726.o6 | 348726o1 | [1, 0, 1, -3619030062, 615395366299744] | [2] | 1455390720 | \(\Gamma_0(N)\)-optimal |
| 348726.o5 | 348726o2 | [1, 0, 1, -132927959342, 18561302360351840] | [2, 2] | 2910781440 | |
| 348726.o2 | 348726o3 | [1, 0, 1, -2123909643262, 1191384900943738400] | [2, 2] | 5821562880 | |
| 348726.o4 | 348726o4 | [1, 0, 1, -210889143902, -5723731367983456] | [2] | 5821562880 | |
| 348726.o1 | 348726o5 | [1, 0, 1, -33982554021322, 76248643432314434384] | [2] | 11643125760 | |
| 348726.o3 | 348726o6 | [1, 0, 1, -2120972207922, 1194844642836517936] | [2] | 11643125760 |
Rank
sage: E.rank()
The elliptic curves in class 348726o have rank \(0\).
Complex multiplication
The elliptic curves in class 348726o do not have complex multiplication.Modular form 348726.2.a.o
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
