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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 259920.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.bq1 | 259920bq4 | \([0, 0, 0, -6585723, -6505089318]\) | \(899466517764/95\) | \(3336358388382720\) | \([2]\) | \(5898240\) | \(2.4068\) | |
| 259920.bq2 | 259920bq3 | \([0, 0, 0, -737523, 80373762]\) | \(1263284964/651605\) | \(22884082185917076480\) | \([2]\) | \(5898240\) | \(2.4068\) | |
| 259920.bq3 | 259920bq2 | \([0, 0, 0, -412623, -101115378]\) | \(884901456/9025\) | \(79238511724089600\) | \([2, 2]\) | \(2949120\) | \(2.0603\) | |
| 259920.bq4 | 259920bq1 | \([0, 0, 0, -6498, -3889053]\) | \(-55296/11875\) | \(-6516324977310000\) | \([2]\) | \(1474560\) | \(1.7137\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 259920.bq do not have complex multiplication.Modular form 259920.2.a.bq
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
