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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 11550cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11550.cu4 | 11550cu1 | \([1, 0, 0, -117453, -15503103]\) | \(1433528304665250149/162339408\) | \(20292426000\) | \([2]\) | \(38400\) | \(1.4017\) | \(\Gamma_0(N)\)-optimal |
| 11550.cu3 | 11550cu2 | \([1, 0, 0, -117753, -15420003]\) | \(1444540994277943589/15251205665388\) | \(1906400708173500\) | \([2]\) | \(76800\) | \(1.7483\) | |
| 11550.cu2 | 11550cu3 | \([1, 0, 0, -433978, 93753572]\) | \(72313087342699809269/11447096545640448\) | \(1430887068205056000\) | \([10]\) | \(192000\) | \(2.2064\) | |
| 11550.cu1 | 11550cu4 | \([1, 0, 0, -6654778, 6606931172]\) | \(260744057755293612689909/8504954620259328\) | \(1063119327532416000\) | \([10]\) | \(384000\) | \(2.5530\) |
Rank
sage: E.rank()
The elliptic curves in class 11550cu have rank \(0\).
Complex multiplication
The elliptic curves in class 11550cu do not have complex multiplication.Modular form 11550.2.a.cu
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.
