Show commands for:
SageMath
sage: E = EllipticCurve("8400.co1")
sage: E.isogeny_class()
Elliptic curves in class 8400.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 8400.co1 | 8400cg3 | [0, 1, 0, -45008, 3659988] | [2] | 24576 | |
| 8400.co2 | 8400cg2 | [0, 1, 0, -3008, 47988] | [2, 2] | 12288 | |
| 8400.co3 | 8400cg1 | [0, 1, 0, -1008, -12012] | [2] | 6144 | \(\Gamma_0(N)\)-optimal |
| 8400.co4 | 8400cg4 | [0, 1, 0, 6992, 307988] | [4] | 24576 |
Rank
sage: E.rank()
The elliptic curves in class 8400.co have rank \(0\).
Modular form 8400.2.a.co
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.
