Show commands:
SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 53040.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53040.ci1 | 53040cu4 | \([0, 1, 0, -1097520, -442809132]\) | \(35694515311673154481/10400566692750\) | \(42600721173504000\) | \([2]\) | \(811008\) | \(2.1703\) | |
| 53040.ci2 | 53040cu3 | \([0, 1, 0, -537200, 147772500]\) | \(4185743240664514801/113629394531250\) | \(465426000000000000\) | \([4]\) | \(811008\) | \(2.1703\) | |
| 53040.ci3 | 53040cu2 | \([0, 1, 0, -77520, -5025132]\) | \(12577973014374481/4642947562500\) | \(19017513216000000\) | \([2, 2]\) | \(405504\) | \(1.8238\) | |
| 53040.ci4 | 53040cu1 | \([0, 1, 0, 14960, -549100]\) | \(90391899763439/84690294000\) | \(-346891444224000\) | \([2]\) | \(202752\) | \(1.4772\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53040.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 53040.ci do not have complex multiplication.Modular form 53040.2.a.ci
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.
