Show commands for:
SageMath
sage: E = EllipticCurve("j1")
sage: E.isogeny_class()
Elliptic curves in class 439569.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 439569.j1 | 439569j1 | [1, -1, 1, -82314139667, 9089128172263650] | [2] | 1824915456 | \(\Gamma_0(N)\)-optimal |
| 439569.j2 | 439569j2 | [1, -1, 1, -75999730982, 10542174641221110] | [2] | 3649830912 |
Rank
sage: E.rank()
The elliptic curves in class 439569.j have rank \(0\).
Complex multiplication
The elliptic curves in class 439569.j do not have complex multiplication.Modular form 439569.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
