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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 203280.cm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.cm1 | 203280cu3 | \([0, -1, 0, -515193840, 4501120881600]\) | \(2084105208962185000201/31185000\) | \(226288147599360000\) | \([4]\) | \(35389440\) | \(3.3336\) | |
| 203280.cm2 | 203280cu4 | \([0, -1, 0, -34910960, 57798670272]\) | \(648474704552553481/176469171805080\) | \(1280515696526046535188480\) | \([2]\) | \(35389440\) | \(3.3336\) | |
| 203280.cm3 | 203280cu2 | \([0, -1, 0, -32200560, 70333728192]\) | \(508859562767519881/62240270400\) | \(451634936504706662400\) | \([2, 2]\) | \(17694720\) | \(2.9870\) | |
| 203280.cm4 | 203280cu1 | \([0, -1, 0, -1844080, 1290950080]\) | \(-95575628340361/43812679680\) | \(-317918554630473646080\) | \([2]\) | \(8847360\) | \(2.6405\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 203280.cm have rank \(0\).
Complex multiplication
The elliptic curves in class 203280.cm 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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
