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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 38640.cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38640.cx1 | 38640dc1 | \([0, 1, 0, -1910200, -1016763052]\) | \(188191720927962271801/9422571110400\) | \(38594851268198400\) | \([2]\) | \(663552\) | \(2.2536\) | \(\Gamma_0(N)\)-optimal |
38640.cx2 | 38640dc2 | \([0, 1, 0, -1807800, -1130508972]\) | \(-159520003524722950201/42335913815758080\) | \(-173407902989345095680\) | \([2]\) | \(1327104\) | \(2.6001\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.cx have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.cx do not have complex multiplication.Modular form 38640.2.a.cx
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.