Show commands:
SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 22050do
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22050.fu2 | 22050do1 | \([1, -1, 1, -5375, -63773]\) | \(59319/28\) | \(8104898434500\) | \([2]\) | \(55296\) | \(1.1711\) | \(\Gamma_0(N)\)-optimal |
22050.fu1 | 22050do2 | \([1, -1, 1, -71525, -7340273]\) | \(139798359/98\) | \(28367144520750\) | \([2]\) | \(110592\) | \(1.5177\) |
Rank
sage: E.rank()
The elliptic curves in class 22050do have rank \(0\).
Complex multiplication
The elliptic curves in class 22050do do not have complex multiplication.Modular form 22050.2.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.