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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 54450fq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54450.gd3 | 54450fq1 | \([1, -1, 1, -3290, 88377]\) | \(-121945/32\) | \(-1033174375200\) | \([]\) | \(81000\) | \(1.0222\) | \(\Gamma_0(N)\)-optimal |
| 54450.gd4 | 54450fq2 | \([1, -1, 1, 23935, -652143]\) | \(46969655/32768\) | \(-1057970560204800\) | \([]\) | \(243000\) | \(1.5715\) | |
| 54450.gd2 | 54450fq3 | \([1, -1, 1, -14180, -7665303]\) | \(-25/2\) | \(-25223983769531250\) | \([]\) | \(405000\) | \(1.8269\) | |
| 54450.gd1 | 54450fq4 | \([1, -1, 1, -3417305, -2430690303]\) | \(-349938025/8\) | \(-100895935078125000\) | \([]\) | \(1215000\) | \(2.3762\) |
Rank
sage: E.rank()
The elliptic curves in class 54450fq have rank \(0\).
Complex multiplication
The elliptic curves in class 54450fq do not have complex multiplication.Modular form 54450.2.a.fq
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
