Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 16560ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16560.c2 | 16560ba1 | \([0, 0, 0, -9047403, -13287722598]\) | \(-1015884369980369163/358196480000000\) | \(-28878361869680640000000\) | \([2]\) | \(1354752\) | \(3.0208\) | \(\Gamma_0(N)\)-optimal |
| 16560.c1 | 16560ba2 | \([0, 0, 0, -155305323, -744899090022]\) | \(5138442430700033888523/413281250000000\) | \(33319382400000000000000\) | \([2]\) | \(2709504\) | \(3.3674\) |
Rank
sage: E.rank()
The elliptic curves in class 16560ba have rank \(1\).
Complex multiplication
The elliptic curves in class 16560ba do not have complex multiplication.Modular form 16560.2.a.ba
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.
