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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 38640.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.f1 | 38640bj4 | \([0, -1, 0, -45536, -3195264]\) | \(2549399737314529/388286718750\) | \(1590422400000000\) | \([2]\) | \(196608\) | \(1.6407\) | |
| 38640.f2 | 38640bj2 | \([0, -1, 0, -12416, 487680]\) | \(51682540549249/5249002500\) | \(21499914240000\) | \([2, 2]\) | \(98304\) | \(1.2941\) | |
| 38640.f3 | 38640bj1 | \([0, -1, 0, -12096, 516096]\) | \(47788676405569/579600\) | \(2374041600\) | \([2]\) | \(49152\) | \(0.94755\) | \(\Gamma_0(N)\)-optimal |
| 38640.f4 | 38640bj3 | \([0, -1, 0, 15584, 2346880]\) | \(102181603702751/642612880350\) | \(-2632142357913600\) | \([2]\) | \(196608\) | \(1.6407\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.f have rank \(1\).
Complex multiplication
The elliptic curves in class 38640.f do not have complex multiplication.Modular form 38640.2.a.f
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.
