Show commands:
SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 58800.do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.do1 | 58800gz1 | \([0, -1, 0, -3342208, 2340262912]\) | \(4386781853/27216\) | \(25615481472000000000\) | \([2]\) | \(1843200\) | \(2.5622\) | \(\Gamma_0(N)\)-optimal |
| 58800.do2 | 58800gz2 | \([0, -1, 0, -1382208, 5060742912]\) | \(-310288733/11573604\) | \(-10892983495968000000000\) | \([2]\) | \(3686400\) | \(2.9087\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.do have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.do do not have complex multiplication.Modular form 58800.2.a.do
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.
