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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 42350ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42350.cb2 | 42350ci1 | \([1, 1, 1, 542, -3849]\) | \(397535/392\) | \(-17361297800\) | \([]\) | \(32400\) | \(0.65178\) | \(\Gamma_0(N)\)-optimal |
42350.cb1 | 42350ci2 | \([1, 1, 1, -5508, 218791]\) | \(-417267265/235298\) | \(-10421119004450\) | \([]\) | \(97200\) | \(1.2011\) |
Rank
sage: E.rank()
The elliptic curves in class 42350ci have rank \(0\).
Complex multiplication
The elliptic curves in class 42350ci do not have complex multiplication.Modular form 42350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.