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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 199920.db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 199920.db1 | 199920cn2 | \([0, -1, 0, -2072520, -697637520]\) | \(5956317014383/2172381210\) | \(359069358499940229120\) | \([2]\) | \(6193152\) | \(2.6446\) | |
| 199920.db2 | 199920cn1 | \([0, -1, 0, 397080, -77274000]\) | \(41890384817/39795300\) | \(-6577700440666521600\) | \([2]\) | \(3096576\) | \(2.2980\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 199920.db have rank \(0\).
Complex multiplication
The elliptic curves in class 199920.db do not have complex multiplication.Modular form 199920.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
