Show commands:
SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 100800do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.gb2 | 100800do1 | \([0, 0, 0, -4800, 628000]\) | \(-65536/875\) | \(-163296000000000\) | \([]\) | \(276480\) | \(1.4088\) | \(\Gamma_0(N)\)-optimal |
| 100800.gb1 | 100800do2 | \([0, 0, 0, -724800, 237508000]\) | \(-225637236736/1715\) | \(-320060160000000\) | \([]\) | \(829440\) | \(1.9581\) |
Rank
sage: E.rank()
The elliptic curves in class 100800do have rank \(0\).
Complex multiplication
The elliptic curves in class 100800do do not have complex multiplication.Modular form 100800.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
