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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 11200.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11200.db1 | 11200cp2 | \([0, -1, 0, -393, 3137]\) | \(-262885120/343\) | \(-8780800\) | \([]\) | \(3456\) | \(0.23939\) | |
11200.db2 | 11200cp1 | \([0, -1, 0, 7, 17]\) | \(1280/7\) | \(-179200\) | \([]\) | \(1152\) | \(-0.30991\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11200.db have rank \(1\).
Complex multiplication
The elliptic curves in class 11200.db do not have complex multiplication.Modular form 11200.2.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.