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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 16650.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16650.be1 | 16650bg2 | \([1, -1, 0, -82242, -4796334]\) | \(43206601229/17964018\) | \(25577674066406250\) | \([2]\) | \(102400\) | \(1.8456\) | |
| 16650.be2 | 16650bg1 | \([1, -1, 0, -70992, -7260084]\) | \(27790593389/11988\) | \(17068851562500\) | \([2]\) | \(51200\) | \(1.4990\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16650.be have rank \(1\).
Complex multiplication
The elliptic curves in class 16650.be do not have complex multiplication.Modular form 16650.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
