Show commands:
SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 110400do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 110400.gy2 | 110400do1 | \([0, 1, 0, -3204033, 2300940063]\) | \(-3552342505518244/179863605135\) | \(-184180331658240000000\) | \([2]\) | \(4055040\) | \(2.6491\) | \(\Gamma_0(N)\)-optimal |
| 110400.gy1 | 110400do2 | \([0, 1, 0, -51872033, 143778816063]\) | \(7536914291382802562/17961229575\) | \(36784598169600000000\) | \([2]\) | \(8110080\) | \(2.9957\) |
Rank
sage: E.rank()
The elliptic curves in class 110400do have rank \(1\).
Complex multiplication
The elliptic curves in class 110400do do not have complex multiplication.Modular form 110400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
