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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 164560.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
164560.ci1 | 164560bl1 | \([0, -1, 0, -25468725, 49480488125]\) | \(-251784668965666816/353546875\) | \(-2565447087808000000\) | \([]\) | \(12648960\) | \(2.8047\) | \(\Gamma_0(N)\)-optimal |
164560.ci2 | 164560bl2 | \([0, -1, 0, -18692725, 76375787325]\) | \(-99546392709922816/289614925147075\) | \(-2101536794249123160371200\) | \([]\) | \(37946880\) | \(3.3540\) |
Rank
sage: E.rank()
The elliptic curves in class 164560.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 164560.ci do not have complex multiplication.Modular form 164560.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.