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SageMath
sage: E = EllipticCurve("cm1")
sage: E.isogeny_class()
Elliptic curves in class 203280cm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 203280.dk6 | 203280cm1 | [0, -1, 0, 67720, -1970406480] | [2] | 7372800 | \(\Gamma_0(N)\)-optimal |
| 203280.dk5 | 203280cm2 | [0, -1, 0, -23173960, -42169216208] | [2, 2] | 14745600 | |
| 203280.dk4 | 203280cm3 | [0, -1, 0, -49261560, 70195294512] | [2] | 29491200 | |
| 203280.dk2 | 203280cm4 | [0, -1, 0, -368953240, -2727629416400] | [2, 2] | 29491200 | |
| 203280.dk3 | 203280cm5 | [0, -1, 0, -367123720, -2756020639568] | [2] | 58982400 | |
| 203280.dk1 | 203280cm6 | [0, -1, 0, -5903251240, -174574223474000] | [2] | 58982400 |
Rank
sage: E.rank()
The elliptic curves in class 203280cm have rank \(1\).
Complex multiplication
The elliptic curves in class 203280cm do not have complex multiplication.Modular form 203280.2.a.cm
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
