Show commands:
SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 225600.cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 225600.cn1 | 225600ed4 | \([0, -1, 0, -1203233, -507609663]\) | \(47034153084673/141\) | \(577536000000\) | \([2]\) | \(1572864\) | \(1.9098\) | |
| 225600.cn2 | 225600ed3 | \([0, -1, 0, -99233, -2409663]\) | \(26383748833/14639043\) | \(59961520128000000\) | \([2]\) | \(1572864\) | \(1.9098\) | |
| 225600.cn3 | 225600ed2 | \([0, -1, 0, -75233, -7905663]\) | \(11497268593/19881\) | \(81432576000000\) | \([2, 2]\) | \(786432\) | \(1.5632\) | |
| 225600.cn4 | 225600ed1 | \([0, -1, 0, -3233, -201663]\) | \(-912673/3807\) | \(-15593472000000\) | \([2]\) | \(393216\) | \(1.2166\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 225600.cn have rank \(0\).
Complex multiplication
The elliptic curves in class 225600.cn do not have complex multiplication.Modular form 225600.2.a.cn
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.
