Show commands for:
SageMath
sage: E = EllipticCurve("bl1")
sage: E.isogeny_class()
Elliptic curves in class 45486.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 45486.bl1 | 45486bh4 | [1, -1, 1, -4366724, 3513311435] | [2] | 884736 | |
| 45486.bl2 | 45486bh6 | [1, -1, 1, -2969654, -1950077005] | [2] | 1769472 | |
| 45486.bl3 | 45486bh3 | [1, -1, 1, -337964, 26848523] | [2, 2] | 884736 | |
| 45486.bl4 | 45486bh2 | [1, -1, 1, -272984, 54919883] | [2, 2] | 442368 | |
| 45486.bl5 | 45486bh1 | [1, -1, 1, -13064, 1272395] | [2] | 221184 | \(\Gamma_0(N)\)-optimal |
| 45486.bl6 | 45486bh5 | [1, -1, 1, 1254046, 206427251] | [2] | 1769472 |
Rank
sage: E.rank()
The elliptic curves in class 45486.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 45486.bl do not have complex multiplication.Modular form 45486.2.a.bl
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
