Show commands for:
SageMath
sage: E = EllipticCurve("g1")
sage: E.isogeny_class()
Elliptic curves in class 384.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
384.g1 | 384a1 | [0, 1, 0, -3, -3] | [2] | 16 | \(\Gamma_0(N)\)-optimal |
384.g2 | 384a2 | [0, 1, 0, 7, -9] | [2] | 32 |
Rank
sage: E.rank()
The elliptic curves in class 384.g have rank \(0\).
Complex multiplication
The elliptic curves in class 384.g do not have complex multiplication.Modular form 384.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.