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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 28224.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.bq1 | 28224gb4 | \([0, 0, 0, -7113036, -7301811440]\) | \(7080974546692/189\) | \(1062325247606784\) | \([2]\) | \(589824\) | \(2.3970\) | |
| 28224.bq2 | 28224gb3 | \([0, 0, 0, -692076, 26578384]\) | \(6522128932/3720087\) | \(20909747848644329472\) | \([2]\) | \(589824\) | \(2.3970\) | |
| 28224.bq3 | 28224gb2 | \([0, 0, 0, -445116, -113793680]\) | \(6940769488/35721\) | \(50194867949420544\) | \([2, 2]\) | \(294912\) | \(2.0504\) | |
| 28224.bq4 | 28224gb1 | \([0, 0, 0, -12936, -3674216]\) | \(-2725888/64827\) | \(-5693399373892608\) | \([2]\) | \(147456\) | \(1.7039\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28224.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 28224.bq do not have complex multiplication.Modular form 28224.2.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.
