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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 489762g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
489762.g1 | 489762g1 | \([1, -1, 0, -481311, -128404899]\) | \(-100089230083481353/354923856\) | \(-43726973983056\) | \([]\) | \(3981312\) | \(1.8358\) | \(\Gamma_0(N)\)-optimal* |
489762.g2 | 489762g2 | \([1, -1, 0, -307566, -222312492]\) | \(-26117117748640633/158305301876736\) | \(-19503371496515751936\) | \([]\) | \(11943936\) | \(2.3851\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 489762g have rank \(1\).
Complex multiplication
The elliptic curves in class 489762g do not have complex multiplication.Modular form 489762.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.