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SageMath
E = EllipticCurve("hu1")
E.isogeny_class()
Elliptic curves in class 474320hu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
474320.hu2 | 474320hu1 | \([0, 1, 0, 180, 6488]\) | \(176/5\) | \(-18221477120\) | \([]\) | \(217728\) | \(0.64890\) | \(\Gamma_0(N)\)-optimal* |
474320.hu1 | 474320hu2 | \([0, 1, 0, -21380, 1196600]\) | \(-296587984/125\) | \(-455536928000\) | \([]\) | \(653184\) | \(1.1982\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 474320hu have rank \(1\).
Complex multiplication
The elliptic curves in class 474320hu do not have complex multiplication.Modular form 474320.2.a.hu
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.