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SageMath
E = EllipticCurve("gk1")
E.isogeny_class()
Elliptic curves in class 400752gk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 400752.gk2 | 400752gk1 | \([0, 0, 0, -11113608, 14260367275]\) | \(7346581704933376/275517\) | \(5693142086639568\) | \([2]\) | \(11059200\) | \(2.5156\) | \(\Gamma_0(N)\)-optimal |
| 400752.gk1 | 400752gk2 | \([0, 0, 0, -11129943, 14216344450]\) | \(461188987116496/2811467307\) | \(929515513057584507648\) | \([2]\) | \(22118400\) | \(2.8622\) |
Rank
sage: E.rank()
The elliptic curves in class 400752gk have rank \(0\).
Complex multiplication
The elliptic curves in class 400752gk do not have complex multiplication.Modular form 400752.2.a.gk
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.
