Show commands for:
SageMath
sage: E = EllipticCurve("a1")
sage: E.isogeny_class()
Elliptic curves in class 26.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
26.a1 | 26a2 | [1, 0, 1, -460, -3830] | [] | 6 | |
26.a2 | 26a1 | [1, 0, 1, -5, -8] | [3] | 2 | \(\Gamma_0(N)\)-optimal |
26.a3 | 26a3 | [1, 0, 1, 0, 0] | [3] | 6 |
Rank
sage: E.rank()
The elliptic curves in class 26.a have rank \(0\).
Complex multiplication
The elliptic curves in class 26.a do not have complex multiplication.Modular form 26.2.a.a
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.