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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 5550x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5550.bd3 | 5550x1 | \([1, 1, 1, -7813, 323531]\) | \(-3375675045001/999000000\) | \(-15609375000000\) | \([2]\) | \(24192\) | \(1.2460\) | \(\Gamma_0(N)\)-optimal |
| 5550.bd2 | 5550x2 | \([1, 1, 1, -132813, 18573531]\) | \(16581570075765001/998001000\) | \(15593765625000\) | \([2]\) | \(48384\) | \(1.5926\) | |
| 5550.bd4 | 5550x3 | \([1, 1, 1, 57812, -2695219]\) | \(1367594037332999/995878502400\) | \(-15560601600000000\) | \([2]\) | \(72576\) | \(1.7953\) | |
| 5550.bd1 | 5550x4 | \([1, 1, 1, -262188, -23175219]\) | \(127568139540190201/59114336463360\) | \(923661507240000000\) | \([2]\) | \(145152\) | \(2.1419\) |
Rank
sage: E.rank()
The elliptic curves in class 5550x have rank \(0\).
Complex multiplication
The elliptic curves in class 5550x do not have complex multiplication.Modular form 5550.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
