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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 22848cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22848.cq2 | 22848cp1 | \([0, 1, 0, 63, 1215]\) | \(415292/9639\) | \(-631701504\) | \([2]\) | \(10240\) | \(0.36890\) | \(\Gamma_0(N)\)-optimal |
22848.cq1 | 22848cp2 | \([0, 1, 0, -1377, 18207]\) | \(2204605874/127449\) | \(16704995328\) | \([2]\) | \(20480\) | \(0.71547\) |
Rank
sage: E.rank()
The elliptic curves in class 22848cp have rank \(0\).
Complex multiplication
The elliptic curves in class 22848cp do not have complex multiplication.Modular form 22848.2.a.cp
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.