Show commands:
SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 159600bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159600.gv3 | 159600bn1 | \([0, 1, 0, -64608, 3676788]\) | \(466025146777/177366672\) | \(11351467008000000\) | \([2]\) | \(983040\) | \(1.7800\) | \(\Gamma_0(N)\)-optimal |
| 159600.gv2 | 159600bn2 | \([0, 1, 0, -456608, -116275212]\) | \(164503536215257/4178071044\) | \(267396546816000000\) | \([2, 2]\) | \(1966080\) | \(2.1266\) | |
| 159600.gv4 | 159600bn3 | \([0, 1, 0, 75392, -370571212]\) | \(740480746823/927484650666\) | \(-59359017642624000000\) | \([2]\) | \(3932160\) | \(2.4732\) | |
| 159600.gv1 | 159600bn4 | \([0, 1, 0, -7260608, -7532635212]\) | \(661397832743623417/443352042\) | \(28374530688000000\) | \([2]\) | \(3932160\) | \(2.4732\) |
Rank
sage: E.rank()
The elliptic curves in class 159600bn have rank \(1\).
Complex multiplication
The elliptic curves in class 159600bn do not have complex multiplication.Modular form 159600.2.a.bn
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 Cremona 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 Cremona labels.
