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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 254100.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254100.be1 | 254100be1 | \([0, -1, 0, -1991458, -1152715463]\) | \(-3155449600/250047\) | \(-69214611463593750000\) | \([]\) | \(8748000\) | \(2.5539\) | \(\Gamma_0(N)\)-optimal |
| 254100.be2 | 254100be2 | \([0, -1, 0, 11621042, -458477963]\) | \(627021958400/363182463\) | \(-100531232396053593750000\) | \([]\) | \(26244000\) | \(3.1032\) |
Rank
sage: E.rank()
The elliptic curves in class 254100.be have rank \(0\).
Complex multiplication
The elliptic curves in class 254100.be do not have complex multiplication.Modular form 254100.2.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.
