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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 9800.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9800.x1 | 9800ba3 | \([0, 0, 0, -131075, 18264750]\) | \(132304644/5\) | \(9411920000000\) | \([2]\) | \(27648\) | \(1.5755\) | |
| 9800.x2 | 9800ba2 | \([0, 0, 0, -8575, 257250]\) | \(148176/25\) | \(11764900000000\) | \([2, 2]\) | \(13824\) | \(1.2289\) | |
| 9800.x3 | 9800ba1 | \([0, 0, 0, -2450, -42875]\) | \(55296/5\) | \(147061250000\) | \([2]\) | \(6912\) | \(0.88231\) | \(\Gamma_0(N)\)-optimal |
| 9800.x4 | 9800ba4 | \([0, 0, 0, 15925, 1457750]\) | \(237276/625\) | \(-1176490000000000\) | \([2]\) | \(27648\) | \(1.5755\) |
Rank
sage: E.rank()
The elliptic curves in class 9800.x have rank \(1\).
Complex multiplication
The elliptic curves in class 9800.x do not have complex multiplication.Modular form 9800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
