Show commands for:
SageMath
sage: E = EllipticCurve("ia1")
sage: E.isogeny_class()
Elliptic curves in class 92400.ia
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 92400.ia1 | 92400hd6 | [0, 1, 0, -1219680008, 16394802983988] | [2] | 11796480 | |
| 92400.ia2 | 92400hd4 | [0, 1, 0, -76230008, 256149683988] | [2, 2] | 5898240 | |
| 92400.ia3 | 92400hd5 | [0, 1, 0, -75852008, 258816095988] | [2] | 11796480 | |
| 92400.ia4 | 92400hd3 | [0, 1, 0, -10178008, -6594196012] | [2] | 5898240 | |
| 92400.ia5 | 92400hd2 | [0, 1, 0, -4788008, 3959423988] | [2, 2] | 2949120 | |
| 92400.ia6 | 92400hd1 | [0, 1, 0, 13992, 185051988] | [2] | 1474560 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.ia have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.ia do not have complex multiplication.Modular form 92400.2.a.ia
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
