Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 38640.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.d1 | 38640bg4 | \([0, -1, 0, -736016, -242795520]\) | \(10765299591712341649/20708625\) | \(84822528000\) | \([2]\) | \(270336\) | \(1.7786\) | |
| 38640.d2 | 38640bg2 | \([0, -1, 0, -46016, -3779520]\) | \(2630872462131649/3645140625\) | \(14930496000000\) | \([2, 2]\) | \(135168\) | \(1.4321\) | |
| 38640.d3 | 38640bg3 | \([0, -1, 0, -33136, -5953664]\) | \(-982374577874929/3183837890625\) | \(-13041000000000000\) | \([2]\) | \(270336\) | \(1.7786\) | |
| 38640.d4 | 38640bg1 | \([0, -1, 0, -3696, -21504]\) | \(1363569097969/734582625\) | \(3008850432000\) | \([2]\) | \(67584\) | \(1.0855\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38640.d have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.d do not have complex multiplication.Modular form 38640.2.a.d
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.
