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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 413712.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
413712.g1 | 413712g2 | \([0, 0, 0, -7970547, -2898963470]\) | \(3885442650361/1996623837\) | \(28776889014303256399872\) | \([2]\) | \(49545216\) | \(3.0017\) | \(\Gamma_0(N)\)-optimal* |
413712.g2 | 413712g1 | \([0, 0, 0, -6388707, -6209754590]\) | \(2000852317801/2094417\) | \(30186359814890852352\) | \([2]\) | \(24772608\) | \(2.6551\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 413712.g have rank \(1\).
Complex multiplication
The elliptic curves in class 413712.g do not have complex multiplication.Modular form 413712.2.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.