Show commands for:
SageMath
sage: E = EllipticCurve("t1")
sage: E.isogeny_class()
Elliptic curves in class 303450.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 303450.t1 | 303450t3 | [1, 1, 0, -9710550, 11642949000] | [2] | 10485760 | |
| 303450.t2 | 303450t6 | [1, 1, 0, -6603800, -6471932250] | [2] | 20971520 | |
| 303450.t3 | 303450t4 | [1, 1, 0, -751550, 88440000] | [2, 2] | 10485760 | |
| 303450.t4 | 303450t2 | [1, 1, 0, -607050, 181642500] | [2, 2] | 5242880 | |
| 303450.t5 | 303450t1 | [1, 1, 0, -29050, 4196500] | [2] | 2621440 | \(\Gamma_0(N)\)-optimal |
| 303450.t6 | 303450t5 | [1, 1, 0, 2788700, 686742250] | [2] | 20971520 |
Rank
sage: E.rank()
The elliptic curves in class 303450.t have rank \(1\).
Complex multiplication
The elliptic curves in class 303450.t do not have complex multiplication.Modular form 303450.2.a.t
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.
