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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 3920bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3920.g2 | 3920bg1 | \([0, 1, 0, -800, -327692]\) | \(-49/40\) | \(-46280744796160\) | \([]\) | \(10080\) | \(1.3012\) | \(\Gamma_0(N)\)-optimal |
3920.g1 | 3920bg2 | \([0, 1, 0, -384960, -92065100]\) | \(-5452947409/250\) | \(-289254654976000\) | \([]\) | \(30240\) | \(1.8505\) |
Rank
sage: E.rank()
The elliptic curves in class 3920bg have rank \(0\).
Complex multiplication
The elliptic curves in class 3920bg do not have complex multiplication.Modular form 3920.2.a.bg
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.