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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 38808.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38808.ci1 | 38808bu2 | \([0, 0, 0, -361179, -80774442]\) | \(3203226/121\) | \(196828949783144448\) | \([2]\) | \(387072\) | \(2.0868\) | |
38808.ci2 | 38808bu1 | \([0, 0, 0, 9261, -4537890]\) | \(108/11\) | \(-8946770444688384\) | \([2]\) | \(193536\) | \(1.7403\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38808.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 38808.ci do not have complex multiplication.Modular form 38808.2.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.