Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 206400.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206400.j1 | 206400ia2 | \([0, -1, 0, -11073, -328383]\) | \(4582567781/1198152\) | \(39261044736000\) | \([2]\) | \(589824\) | \(1.3173\) | |
| 206400.j2 | 206400ia1 | \([0, -1, 0, 1727, -33983]\) | \(17373979/24768\) | \(-811597824000\) | \([2]\) | \(294912\) | \(0.97076\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206400.j have rank \(0\).
Complex multiplication
The elliptic curves in class 206400.j do not have complex multiplication.Modular form 206400.2.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.
