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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 38640.cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38640.cz1 | 38640da1 | \([0, 1, 0, -82640, 9109908]\) | \(15238420194810961/12619514880\) | \(51689532948480\) | \([2]\) | \(161280\) | \(1.5597\) | \(\Gamma_0(N)\)-optimal |
38640.cz2 | 38640da2 | \([0, 1, 0, -64720, 13188500]\) | \(-7319577278195281/14169067365600\) | \(-58036499929497600\) | \([2]\) | \(322560\) | \(1.9063\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.cz have rank \(1\).
Complex multiplication
The elliptic curves in class 38640.cz do not have complex multiplication.Modular form 38640.2.a.cz
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.