Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 16820a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16820.a1 | 16820a1 | \([0, 0, 0, -6728, -170723]\) | \(3538944/725\) | \(6899950523600\) | \([2]\) | \(20160\) | \(1.1790\) | \(\Gamma_0(N)\)-optimal |
| 16820.a2 | 16820a2 | \([0, 0, 0, 14297, -1024338]\) | \(2122416/4205\) | \(-640315408590080\) | \([2]\) | \(40320\) | \(1.5256\) |
Rank
sage: E.rank()
The elliptic curves in class 16820a have rank \(0\).
Complex multiplication
The elliptic curves in class 16820a do not have complex multiplication.Modular form 16820.2.a.a
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.
