Show commands for:
SageMath
sage: E = EllipticCurve("16830.h1")
sage: E.isogeny_class()
sage: E.isogeny_class()
Elliptic curves in class 16830k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion order | Modular degree | Optimality |
|---|---|---|---|---|---|
| 16830.h2 | 16830k1 | [1, -1, 0, 705, 3501] | 3 | 14400 | \(\Gamma_0(N)\)-optimal |
| 16830.h1 | 16830k2 | [1, -1, 0, -7710, -318700] | 1 | 43200 |
Rank
sage: E.rank()
The elliptic curves in class 16830k have rank \(1\).
Modular form 16830.2.a.h
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
