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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 92736cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92736.dn2 | 92736cj1 | \([0, 0, 0, 19860, -5067344]\) | \(4533086375/60669952\) | \(-11594208380977152\) | \([2]\) | \(516096\) | \(1.7632\) | \(\Gamma_0(N)\)-optimal |
| 92736.dn1 | 92736cj2 | \([0, 0, 0, -348780, -74224208]\) | \(24553362849625/1755162752\) | \(335416825271549952\) | \([2]\) | \(1032192\) | \(2.1098\) |
Rank
sage: E.rank()
The elliptic curves in class 92736cj have rank \(0\).
Complex multiplication
The elliptic curves in class 92736cj do not have complex multiplication.Modular form 92736.2.a.cj
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.
