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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 209814ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
209814.a1 | 209814ci1 | \([1, 1, 0, -6854652, 6900354960]\) | \(832972004929/610368\) | \(26100053396599566912\) | \([2]\) | \(13271040\) | \(2.6599\) | \(\Gamma_0(N)\)-optimal |
209814.a2 | 209814ci2 | \([1, 1, 0, -5455892, 9799984440]\) | \(-420021471169/727634952\) | \(-31114526155421258704968\) | \([2]\) | \(26542080\) | \(3.0065\) |
Rank
sage: E.rank()
The elliptic curves in class 209814ci have rank \(2\).
Complex multiplication
The elliptic curves in class 209814ci do not have complex multiplication.Modular form 209814.2.a.ci
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.