Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 41280.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41280.bu1 | 41280u4 | \([0, -1, 0, -53665, 4770337]\) | \(65202655558249/512820150\) | \(134432725401600\) | \([4]\) | \(147456\) | \(1.5392\) | |
| 41280.bu2 | 41280u2 | \([0, -1, 0, -5665, -39263]\) | \(76711450249/41602500\) | \(10905845760000\) | \([2, 2]\) | \(73728\) | \(1.1926\) | |
| 41280.bu3 | 41280u1 | \([0, -1, 0, -4385, -110175]\) | \(35578826569/51600\) | \(13526630400\) | \([2]\) | \(36864\) | \(0.84606\) | \(\Gamma_0(N)\)-optimal |
| 41280.bu4 | 41280u3 | \([0, -1, 0, 21855, -330975]\) | \(4403686064471/2721093750\) | \(-713318400000000\) | \([2]\) | \(147456\) | \(1.5392\) |
Rank
sage: E.rank()
The elliptic curves in class 41280.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 41280.bu do not have complex multiplication.Modular form 41280.2.a.bu
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.
