Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 262392.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 262392.bb1 | 262392bb4 | \([0, 1, 0, -255944, -48702528]\) | \(3044193988/85293\) | \(51951887890486272\) | \([2]\) | \(3211264\) | \(1.9865\) | |
| 262392.bb2 | 262392bb2 | \([0, 1, 0, -37284, 1676736]\) | \(37642192/13689\) | \(2084489328939264\) | \([2, 2]\) | \(1605632\) | \(1.6399\) | |
| 262392.bb3 | 262392bb1 | \([0, 1, 0, -33079, 2304122]\) | \(420616192/117\) | \(1113509256912\) | \([2]\) | \(802816\) | \(1.2933\) | \(\Gamma_0(N)\)-optimal |
| 262392.bb4 | 262392bb3 | \([0, 1, 0, 114096, 11970576]\) | \(269676572/257049\) | \(-156568309595882496\) | \([2]\) | \(3211264\) | \(1.9865\) |
Rank
sage: E.rank()
The elliptic curves in class 262392.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 262392.bb do not have complex multiplication.Modular form 262392.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
