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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 494190.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
494190.db1 | 494190db2 | \([1, -1, 1, -4209773, -3323488219]\) | \(468898230633769/5540400\) | \(97490472932660400\) | \([2]\) | \(15728640\) | \(2.4099\) | \(\Gamma_0(N)\)-optimal* |
494190.db2 | 494190db1 | \([1, -1, 1, -256253, -54717883]\) | \(-105756712489/12476160\) | \(-219534102011324160\) | \([2]\) | \(7864320\) | \(2.0633\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 494190.db have rank \(1\).
Complex multiplication
The elliptic curves in class 494190.db do not have complex multiplication.Modular form 494190.2.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.