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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 38640.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.cl1 | 38640cp1 | \([0, 1, 0, -17251536, -27585464940]\) | \(138626767243242683688529/5300196249600\) | \(21709603838361600\) | \([2]\) | \(1105920\) | \(2.6260\) | \(\Gamma_0(N)\)-optimal |
| 38640.cl2 | 38640cp2 | \([0, 1, 0, -17225936, -27671388780]\) | \(-138010547060620856386129/857302254769101120\) | \(-3511510035534238187520\) | \([2]\) | \(2211840\) | \(2.9725\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.cl have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.cl do not have complex multiplication.Modular form 38640.2.a.cl
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.
