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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 189618.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 189618.g1 | 189618bo1 | \([1, 1, 0, -14253125, -20716222899]\) | \(66342819962001390625/4812668669952\) | \(23229832450142343168\) | \([2]\) | \(9934848\) | \(2.7672\) | \(\Gamma_0(N)\)-optimal |
| 189618.g2 | 189618bo2 | \([1, 1, 0, -13333765, -23503170803]\) | \(-54315282059491182625/17983956399469632\) | \(-86805122604567614964288\) | \([2]\) | \(19869696\) | \(3.1137\) |
Rank
sage: E.rank()
The elliptic curves in class 189618.g have rank \(1\).
Complex multiplication
The elliptic curves in class 189618.g do not have complex multiplication.Modular form 189618.2.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 LMFDB 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 LMFDB labels.
