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SageMath
E = EllipticCurve("jw1")
E.isogeny_class()
Elliptic curves in class 202800.jw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.jw1 | 202800bg2 | \([0, 1, 0, -238156208, -1410212138412]\) | \(38686490446661/141927552\) | \(5480457482732544000000000\) | \([2]\) | \(72253440\) | \(3.6074\) | |
| 202800.jw2 | 202800bg1 | \([0, 1, 0, -21836208, 626901588]\) | \(29819839301/17252352\) | \(666190463238144000000000\) | \([2]\) | \(36126720\) | \(3.2608\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.jw have rank \(0\).
Complex multiplication
The elliptic curves in class 202800.jw do not have complex multiplication.Modular form 202800.2.a.jw
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.
