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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 187200db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.cx2 | 187200db1 | \([0, 0, 0, -204654540, -1234551966320]\) | \(-198417696411528597145/22989483914821632\) | \(-109833969820663609609420800\) | \([]\) | \(51609600\) | \(3.7330\) | \(\Gamma_0(N)\)-optimal |
187200.cx1 | 187200db2 | \([0, 0, 0, -131274007500, -18306959838950000]\) | \(-134057911417971280740025/1872\) | \(-3493601280000000000\) | \([]\) | \(258048000\) | \(4.5378\) |
Rank
sage: E.rank()
The elliptic curves in class 187200db have rank \(1\).
Complex multiplication
The elliptic curves in class 187200db do not have complex multiplication.Modular form 187200.2.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 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.