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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 9408.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9408.db1 | 9408bk2 | \([0, 1, 0, -2231329, 1288709183]\) | \(-16591834777/98304\) | \(-7279331738306740224\) | \([]\) | \(241920\) | \(2.4596\) | |
9408.db2 | 9408bk1 | \([0, 1, 0, 73631, 9456383]\) | \(596183/864\) | \(-63978501606211584\) | \([]\) | \(80640\) | \(1.9103\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9408.db have rank \(1\).
Complex multiplication
The elliptic curves in class 9408.db do not have complex multiplication.Modular form 9408.2.a.db
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.