Show commands:
SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 115920.da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.da1 | 115920ea4 | \([0, 0, 0, -409827, 86681954]\) | \(2549399737314529/388286718750\) | \(1159417929600000000\) | \([2]\) | \(1572864\) | \(2.1900\) | |
| 115920.da2 | 115920ea2 | \([0, 0, 0, -111747, -13055614]\) | \(51682540549249/5249002500\) | \(15673437480960000\) | \([2, 2]\) | \(786432\) | \(1.8434\) | |
| 115920.da3 | 115920ea1 | \([0, 0, 0, -108867, -13825726]\) | \(47788676405569/579600\) | \(1730676326400\) | \([2]\) | \(393216\) | \(1.4969\) | \(\Gamma_0(N)\)-optimal |
| 115920.da4 | 115920ea3 | \([0, 0, 0, 140253, -63506014]\) | \(102181603702751/642612880350\) | \(-1918831778919014400\) | \([2]\) | \(1572864\) | \(2.1900\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.da have rank \(2\).
Complex multiplication
The elliptic curves in class 115920.da do not have complex multiplication.Modular form 115920.2.a.da
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.
