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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 388080.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.ci1 | 388080ci1 | \([0, 0, 0, -6048, 117747]\) | \(226492416/75625\) | \(8169035490000\) | \([2]\) | \(737280\) | \(1.1802\) | \(\Gamma_0(N)\)-optimal |
388080.ci2 | 388080ci2 | \([0, 0, 0, 17577, 812322]\) | \(347482224/366025\) | \(-632610108345600\) | \([2]\) | \(1474560\) | \(1.5268\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.ci do not have complex multiplication.Modular form 388080.2.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 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.