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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 228888.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
228888.be1 | 228888bt1 | \([0, 0, 0, -21675, -363562]\) | \(62500/33\) | \(594613757371392\) | \([2]\) | \(655360\) | \(1.5265\) | \(\Gamma_0(N)\)-optimal |
228888.be2 | 228888bt2 | \([0, 0, 0, 82365, -2839714]\) | \(1714750/1089\) | \(-39244507986511872\) | \([2]\) | \(1310720\) | \(1.8730\) |
Rank
sage: E.rank()
The elliptic curves in class 228888.be have rank \(1\).
Complex multiplication
The elliptic curves in class 228888.be do not have complex multiplication.Modular form 228888.2.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.