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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 28224bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.cq4 | 28224bo1 | \([0, 0, 0, 11760, -167384]\) | \(2048000/1323\) | \(-116191823956992\) | \([2]\) | \(73728\) | \(1.3878\) | \(\Gamma_0(N)\)-optimal |
| 28224.cq3 | 28224bo2 | \([0, 0, 0, -49980, -1377488]\) | \(9826000/5103\) | \(7170695421345792\) | \([2]\) | \(147456\) | \(1.7343\) | |
| 28224.cq2 | 28224bo3 | \([0, 0, 0, -199920, -35433272]\) | \(-10061824000/352947\) | \(-30997396591193088\) | \([2]\) | \(221184\) | \(1.9371\) | |
| 28224.cq1 | 28224bo4 | \([0, 0, 0, -3225180, -2229351824]\) | \(2640279346000/3087\) | \(4337828094394368\) | \([2]\) | \(442368\) | \(2.2836\) |
Rank
sage: E.rank()
The elliptic curves in class 28224bo have rank \(1\).
Complex multiplication
The elliptic curves in class 28224bo do not have complex multiplication.Modular form 28224.2.a.bo
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
