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SageMath
sage: E = EllipticCurve("16830.g1")
sage: E.isogeny_class()
Elliptic curves in class 16830u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 16830.g2 | 16830u1 | [1, -1, 0, -7920, -117504] | [2] | 43008 | \(\Gamma_0(N)\)-optimal |
| 16830.g1 | 16830u2 | [1, -1, 0, -105840, -13219200] | [2] | 86016 |
Rank
sage: E.rank()
The elliptic curves in class 16830u have rank \(1\).
Modular form 16830.2.a.g
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.
