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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 16800.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16800.x1 | 16800j3 | \([0, -1, 0, -28008, 1813512]\) | \(303735479048/105\) | \(840000000\) | \([2]\) | \(36864\) | \(1.0683\) | |
| 16800.x2 | 16800j2 | \([0, -1, 0, -3633, -40863]\) | \(82881856/36015\) | \(2304960000000\) | \([2]\) | \(36864\) | \(1.0683\) | |
| 16800.x3 | 16800j1 | \([0, -1, 0, -1758, 28512]\) | \(601211584/11025\) | \(11025000000\) | \([2, 2]\) | \(18432\) | \(0.72173\) | \(\Gamma_0(N)\)-optimal |
| 16800.x4 | 16800j4 | \([0, -1, 0, -8, 81012]\) | \(-8/354375\) | \(-2835000000000\) | \([2]\) | \(36864\) | \(1.0683\) |
Rank
sage: E.rank()
The elliptic curves in class 16800.x have rank \(0\).
Complex multiplication
The elliptic curves in class 16800.x do not have complex multiplication.Modular form 16800.2.a.x
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.
