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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 22800dh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22800.cj4 | 22800dh1 | \([0, 1, 0, 3733992, 5906531988]\) | \(89962967236397039/287450726400000\) | \(-18396846489600000000000\) | \([2]\) | \(1382400\) | \(2.9554\) | \(\Gamma_0(N)\)-optimal |
| 22800.cj3 | 22800dh2 | \([0, 1, 0, -35178008, 69177443988]\) | \(75224183150104868881/11219310000000000\) | \(718035840000000000000000\) | \([2]\) | \(2764800\) | \(3.3020\) | |
| 22800.cj2 | 22800dh3 | \([0, 1, 0, -1320586008, 18470895011988]\) | \(-3979640234041473454886161/1471455901872240\) | \(-94173177719823360000000\) | \([2]\) | \(6912000\) | \(3.7601\) | |
| 22800.cj1 | 22800dh4 | \([0, 1, 0, -21129378008, 1182158189843988]\) | \(16300610738133468173382620881/2228489100\) | \(142623302400000000\) | \([2]\) | \(13824000\) | \(4.1067\) |
Rank
sage: E.rank()
The elliptic curves in class 22800dh have rank \(0\).
Complex multiplication
The elliptic curves in class 22800dh do not have complex multiplication.Modular form 22800.2.a.dh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
