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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 40950x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40950.bg4 | 40950x1 | \([1, -1, 0, 1458, -709884]\) | \(30080231/19110000\) | \(-217674843750000\) | \([2]\) | \(147456\) | \(1.4302\) | \(\Gamma_0(N)\)-optimal |
| 40950.bg3 | 40950x2 | \([1, -1, 0, -111042, -13872384]\) | \(13293525831769/365192100\) | \(4159766264062500\) | \([2, 2]\) | \(294912\) | \(1.7768\) | |
| 40950.bg2 | 40950x3 | \([1, -1, 0, -257292, 30441366]\) | \(165369706597369/60703354530\) | \(691449147693281250\) | \([2]\) | \(589824\) | \(2.1234\) | |
| 40950.bg1 | 40950x4 | \([1, -1, 0, -1764792, -901936134]\) | \(53365044437418169/41984670\) | \(478231631718750\) | \([2]\) | \(589824\) | \(2.1234\) |
Rank
sage: E.rank()
The elliptic curves in class 40950x have rank \(0\).
Complex multiplication
The elliptic curves in class 40950x do not have complex multiplication.Modular form 40950.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
