Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 17600.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17600.bu1 | 17600j4 | \([0, 0, 0, -94700, 11214000]\) | \(22930509321/6875\) | \(28160000000000\) | \([2]\) | \(49152\) | \(1.5588\) | |
| 17600.bu2 | 17600j3 | \([0, 0, 0, -46700, -3794000]\) | \(2749884201/73205\) | \(299847680000000\) | \([2]\) | \(49152\) | \(1.5588\) | |
| 17600.bu3 | 17600j2 | \([0, 0, 0, -6700, 126000]\) | \(8120601/3025\) | \(12390400000000\) | \([2, 2]\) | \(24576\) | \(1.2122\) | |
| 17600.bu4 | 17600j1 | \([0, 0, 0, 1300, 14000]\) | \(59319/55\) | \(-225280000000\) | \([2]\) | \(12288\) | \(0.86563\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17600.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 17600.bu do not have complex multiplication.Modular form 17600.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
