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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 54450.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54450.be1 | 54450df2 | \([1, -1, 0, -136692, -19418184]\) | \(-349938025/8\) | \(-6457339845000\) | \([]\) | \(243000\) | \(1.5715\) | |
| 54450.be2 | 54450df3 | \([1, -1, 0, -82242, 10964916]\) | \(-121945/32\) | \(-16143349612500000\) | \([]\) | \(405000\) | \(1.8269\) | |
| 54450.be3 | 54450df1 | \([1, -1, 0, -567, -61209]\) | \(-25/2\) | \(-1614334961250\) | \([]\) | \(81000\) | \(1.0222\) | \(\Gamma_0(N)\)-optimal |
| 54450.be4 | 54450df4 | \([1, -1, 0, 598383, -80919459]\) | \(46969655/32768\) | \(-16530790003200000000\) | \([]\) | \(1215000\) | \(2.3762\) |
Rank
sage: E.rank()
The elliptic curves in class 54450.be have rank \(0\).
Complex multiplication
The elliptic curves in class 54450.be do not have complex multiplication.Modular form 54450.2.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.
\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
