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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 9664g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9664.e1 | 9664g1 | \([0, -1, 0, -14721, -684767]\) | \(-1345938541921/4947968\) | \(-1297080123392\) | \([]\) | \(23040\) | \(1.1848\) | \(\Gamma_0(N)\)-optimal |
| 9664.e2 | 9664g2 | \([0, -1, 0, 105599, 14339873]\) | \(496774270317599/628021806008\) | \(-164632148314161152\) | \([]\) | \(115200\) | \(1.9895\) |
Rank
sage: E.rank()
The elliptic curves in class 9664g have rank \(0\).
Complex multiplication
The elliptic curves in class 9664g do not have complex multiplication.Modular form 9664.2.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 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.
