Show commands for:
SageMath
sage: E = EllipticCurve("c1")
sage: E.isogeny_class()
Elliptic curves in class 5610.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
5610.c1 | 5610a4 | [1, 1, 0, -11968, 498988] | [2] | 8192 | |
5610.c2 | 5610a3 | [1, 1, 0, -1048, 532] | [2] | 8192 | |
5610.c3 | 5610a2 | [1, 1, 0, -748, 7552] | [2, 2] | 4096 | |
5610.c4 | 5610a1 | [1, 1, 0, -28, 208] | [2] | 2048 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5610.c have rank \(1\).
Complex multiplication
The elliptic curves in class 5610.c do not have complex multiplication.Modular form 5610.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.