Show commands:
SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 141960.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141960.ci1 | 141960bf3 | \([0, 1, 0, -228490760, 1329309765408]\) | \(266912903848829942596/152163375\) | \(752090673070464000\) | \([2]\) | \(14450688\) | \(3.1911\) | |
| 141960.ci2 | 141960bf2 | \([0, 1, 0, -14283260, 20758989408]\) | \(260798860029250384/196803140625\) | \(243182379621636000000\) | \([2, 2]\) | \(7225344\) | \(2.8445\) | |
| 141960.ci3 | 141960bf4 | \([0, 1, 0, -11325760, 29605463408]\) | \(-32506165579682596/57814914850875\) | \(-285759028568511598464000\) | \([2]\) | \(14450688\) | \(3.1911\) | |
| 141960.ci4 | 141960bf1 | \([0, 1, 0, -1080135, 177958158]\) | \(1804588288006144/866455078125\) | \(66915410707031250000\) | \([2]\) | \(3612672\) | \(2.4979\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141960.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 141960.ci do not have complex multiplication.Modular form 141960.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
