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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 193600.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.db1 | 193600bv1 | \([0, -1, 0, -197633, 92447137]\) | \(-117649/440\) | \(-3192778096640000000\) | \([]\) | \(2211840\) | \(2.2363\) | \(\Gamma_0(N)\)-optimal |
193600.db2 | 193600bv2 | \([0, -1, 0, 1738367, -2193968863]\) | \(80062991/332750\) | \(-2414538435584000000000\) | \([]\) | \(6635520\) | \(2.7856\) |
Rank
sage: E.rank()
The elliptic curves in class 193600.db have rank \(1\).
Complex multiplication
The elliptic curves in class 193600.db do not have complex multiplication.Modular form 193600.2.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.