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SageMath
sage: E = EllipticCurve("q1")
sage: E.isogeny_class()
Elliptic curves in class 1050.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1050.q1 | 1050p3 | \([1, 0, 0, -9338, 346542]\) | \(5763259856089/5670\) | \(88593750\) | \([2]\) | \(1536\) | \(0.81830\) | |
| 1050.q2 | 1050p2 | \([1, 0, 0, -588, 5292]\) | \(1439069689/44100\) | \(689062500\) | \([2, 2]\) | \(768\) | \(0.47173\) | |
| 1050.q3 | 1050p1 | \([1, 0, 0, -88, -208]\) | \(4826809/1680\) | \(26250000\) | \([2]\) | \(384\) | \(0.12515\) | \(\Gamma_0(N)\)-optimal |
| 1050.q4 | 1050p4 | \([1, 0, 0, 162, 18042]\) | \(30080231/9003750\) | \(-140683593750\) | \([2]\) | \(1536\) | \(0.81830\) |
Rank
sage: E.rank()
The elliptic curves in class 1050.q have rank \(0\).
Complex multiplication
The elliptic curves in class 1050.q do not have complex multiplication.Modular form 1050.2.a.q
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.
