Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 200400.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200400.j1 | 200400bc1 | \([0, -1, 0, -728, 7152]\) | \(83453453/8016\) | \(4104192000\) | \([2]\) | \(138240\) | \(0.58220\) | \(\Gamma_0(N)\)-optimal |
200400.j2 | 200400bc2 | \([0, -1, 0, 872, 32752]\) | \(143055667/1004004\) | \(-514050048000\) | \([2]\) | \(276480\) | \(0.92877\) |
Rank
sage: E.rank()
The elliptic curves in class 200400.j have rank \(0\).
Complex multiplication
The elliptic curves in class 200400.j do not have complex multiplication.Modular form 200400.2.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.