Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 22050f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22050.by2 | 22050f1 | \([1, -1, 0, -1258917, 509054741]\) | \(17779581/1280\) | \(15885600931620000000\) | \([2]\) | \(516096\) | \(2.4310\) | \(\Gamma_0(N)\)-optimal |
| 22050.by1 | 22050f2 | \([1, -1, 0, -19780917, 33867176741]\) | \(68971442301/400\) | \(4964250291131250000\) | \([2]\) | \(1032192\) | \(2.7776\) |
Rank
sage: E.rank()
The elliptic curves in class 22050f have rank \(0\).
Complex multiplication
The elliptic curves in class 22050f do not have complex multiplication.Modular form 22050.2.a.f
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.
