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SageMath
sage: E = EllipticCurve("oq1")
sage: E.isogeny_class()
Elliptic curves in class 388080oq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
388080.oq2 | 388080oq1 | [0, 0, 0, -63082992, -225841753424] | [] | 92160000 | \(\Gamma_0(N)\)-optimal |
388080.oq1 | 388080oq2 | [0, 0, 0, -189032592, 18912291835696] | [] | 460800000 |
Rank
sage: E.rank()
The elliptic curves in class 388080oq have rank \(0\).
Complex multiplication
The elliptic curves in class 388080oq do not have complex multiplication.Modular form 388080.2.a.oq
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.