Show commands for:
SageMath
sage: E = EllipticCurve("a1")
sage: E.isogeny_class()
Elliptic curves in class 360.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
360.a1 | 360e3 | [0, 0, 0, -963, 11502] | [2] | 128 | |
360.a2 | 360e2 | [0, 0, 0, -63, 162] | [2, 2] | 64 | |
360.a3 | 360e1 | [0, 0, 0, -18, -27] | [2] | 32 | \(\Gamma_0(N)\)-optimal |
360.a4 | 360e4 | [0, 0, 0, 117, 918] | [2] | 128 |
Rank
sage: E.rank()
The elliptic curves in class 360.a have rank \(1\).
Complex multiplication
The elliptic curves in class 360.a do not have complex multiplication.Modular form 360.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.