Show commands:
SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 91728.fc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91728.fc1 | 91728ef4 | \([0, 0, 0, -490539, 132235418]\) | \(37159393753/1053\) | \(369916827291648\) | \([2]\) | \(589824\) | \(1.8970\) | |
| 91728.fc2 | 91728ef3 | \([0, 0, 0, -137739, -17817478]\) | \(822656953/85683\) | \(30100269242953728\) | \([2]\) | \(589824\) | \(1.8970\) | |
| 91728.fc3 | 91728ef2 | \([0, 0, 0, -31899, 1889930]\) | \(10218313/1521\) | \(534324306087936\) | \([2, 2]\) | \(294912\) | \(1.5505\) | |
| 91728.fc4 | 91728ef1 | \([0, 0, 0, 3381, 161210]\) | \(12167/39\) | \(-13700623233024\) | \([2]\) | \(147456\) | \(1.2039\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91728.fc have rank \(0\).
Complex multiplication
The elliptic curves in class 91728.fc do not have complex multiplication.Modular form 91728.2.a.fc
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.
