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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 75456.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75456.cj1 | 75456ci2 | \([0, 0, 0, -130777932, -575637671792]\) | \(1294373635812597347281/2083292441154\) | \(398123385382834274304\) | \([]\) | \(6451200\) | \(3.2171\) | |
| 75456.cj2 | 75456ci1 | \([0, 0, 0, -1229772, 498920848]\) | \(1076291879750641/60150618144\) | \(11494962135557996544\) | \([]\) | \(1290240\) | \(2.4124\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 75456.cj have rank \(1\).
Complex multiplication
The elliptic curves in class 75456.cj do not have complex multiplication.Modular form 75456.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
