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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 3920.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3920.be1 | 3920r2 | \([0, -1, 0, -7856, 270656]\) | \(-5452947409/250\) | \(-2458624000\) | \([]\) | \(4320\) | \(0.87754\) | |
3920.be2 | 3920r1 | \([0, -1, 0, -16, 960]\) | \(-49/40\) | \(-393379840\) | \([]\) | \(1440\) | \(0.32823\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3920.be have rank \(0\).
Complex multiplication
The elliptic curves in class 3920.be do not have complex multiplication.Modular form 3920.2.a.be
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.