Show commands:
SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 11970.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11970.bo1 | 11970bi4 | \([1, -1, 1, -116993, -11468519]\) | \(8997224809453803/2305248169000\) | \(45374199710427000\) | \([2]\) | \(186624\) | \(1.9056\) | |
| 11970.bo2 | 11970bi2 | \([1, -1, 1, -40553, 3152297]\) | \(273161111316733107/108726499840\) | \(2935615495680\) | \([6]\) | \(62208\) | \(1.3563\) | |
| 11970.bo3 | 11970bi1 | \([1, -1, 1, -2153, 64937]\) | \(-40860428336307/42709811200\) | \(-1153164902400\) | \([6]\) | \(31104\) | \(1.0097\) | \(\Gamma_0(N)\)-optimal |
| 11970.bo4 | 11970bi3 | \([1, -1, 1, 18007, -1154519]\) | \(32807952226197/48013000000\) | \(-945039879000000\) | \([2]\) | \(93312\) | \(1.5590\) |
Rank
sage: E.rank()
The elliptic curves in class 11970.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 11970.bo do not have complex multiplication.Modular form 11970.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
