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SageMath
E = EllipticCurve("gq1")
E.isogeny_class()
Elliptic curves in class 284592.gq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 284592.gq1 | 284592gq2 | \([0, 1, 0, -5364, 138312]\) | \(109744/9\) | \(1400015054592\) | \([2]\) | \(537600\) | \(1.0732\) | |
| 284592.gq2 | 284592gq1 | \([0, 1, 0, -1129, -12454]\) | \(16384/3\) | \(29166980304\) | \([2]\) | \(268800\) | \(0.72659\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 284592.gq have rank \(1\).
Complex multiplication
The elliptic curves in class 284592.gq do not have complex multiplication.Modular form 284592.2.a.gq
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.
