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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 16562e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16562.m4 | 16562e1 | \([1, -1, 0, 7173934, -5021965740]\) | \(71903073502287/60782804992\) | \(-34516686007761000988672\) | \([2]\) | \(1451520\) | \(3.0123\) | \(\Gamma_0(N)\)-optimal |
| 16562.m3 | 16562e2 | \([1, -1, 0, -35224786, -44172943788]\) | \(8511781274893233/3440817243136\) | \(1953934314269415961240576\) | \([2, 2]\) | \(2903040\) | \(3.3589\) | |
| 16562.m1 | 16562e3 | \([1, -1, 0, -489686066, -4169317982348]\) | \(22868021811807457713/8953460393696\) | \(5084394856946864911533536\) | \([2]\) | \(5806080\) | \(3.7054\) | |
| 16562.m2 | 16562e4 | \([1, -1, 0, -259143026, 1574800715060]\) | \(3389174547561866673/74853681183008\) | \(42507103945910228998519328\) | \([2]\) | \(5806080\) | \(3.7054\) |
Rank
sage: E.rank()
The elliptic curves in class 16562e have rank \(0\).
Complex multiplication
The elliptic curves in class 16562e do not have complex multiplication.Modular form 16562.2.a.e
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.
